Not all of DNA appears to be “code” - much of it seems to be “junk” or non-coding. But the parts that do code for something - the genes - collectively the genome - constitute a program, or better: many subprograms for the construction of various organs and therefore organ systems that together constitute a complicated organism. In the case of the human being there must exist subprograms for the structure of the eye, the skin, the liver and bones and so on for every part of the body that can be distinguished from every other part. This includes, of course, that most important part of the human: the brain. While our eyes share many features - though not all - with other animals, our brains, though anatomically similar in many ways to some other large mammals, must be in one sense sharply different. What they are doing is different - which is to say, what the mind is, is different. The software running on the hardware that is the brain is different. If animals have other minds at all (I tend to think they must) they are completely different from our own. They are not a little different (as their eyes or brains are) they are very, very different. Qualitatively different. Of an order altogether unlike anything else in nature. There is something very special about human brains compared to insect brains or dog brains or dolphin and chimp brains. Our brains - or at least the minds that run upon them - are universal. While dogs and chimps and dolphins may have some internal subjective experience of the world, their minds are limited. They can solve problems only of the sort already coded in their genes. Dogs may learn tricks - but the repertoire of possible tricks it can learn is forever bounded by the behaviours coded in its genes. It cannot, for example, learn to write a sonnet, or a computer program or how to engineer itself a better home.
It is important to recognise, brains are not minds: minds are the software, brains are the physical stuff made of neurones. Minds are made of thoughts (both conscious and unconscious). Brain and minds are different things even if necessarily connected in humans. Our minds, the minds of humans running on those human brains - are universal. This means they (those minds) can turn their attention to any problem whatever and attempt a solution. What they possess is the ability to create new knowledge. This unique creative ability makes them universal. This is why the human environment is shaped by humans to a degree not seen in other species. Most other species are victims of their environment, not us: we are masters of it and gaining ever greater mastery over it.
Whatever the program is for this universal intelligence, it is instantiated in our genes. That code, written in the so called "AGTC" code of base pairs codes in part, somewhere, somehow for this special universal capacity only humans possess: this capacity to create new explanatory knowledge to allow us to control the world around us. An amazing code, but a code it is. And so it must be the case that we can write that code into an algorithm that can be then coded by software engineers one day, to produce an artificial general intelligence (AGI). What an AGI is not, is simply an AI who is better than us as chess, and at doing long division and at translating Japanese into Spanish and…(iterate for all other human intellectual abilities). No: it’s not like a million AIs working in parallel. Instead an AGI will be a universal explainer. It won’t be preprogrammed with all possible games and languages and mathematical things we know of (though it could be, I suppose) - what makes the crucial difference is the (as yet known) code that allows it to be a universal explainer. It, like us, will be able to learn things not already in its code. Whatever that code is - being universal (which means able to, in principle, creatively solve any solvable problem including especially problems not yet known) - there cannot be fundamental differences between alternative ways of writing that code. Different ways of coding the same algorithm might appear different (as the numeral 1 appears different to the characters “one” which again seems different to the strings 2/2 or 4-3) but ultimately they will represent exactly the same underlying abstract structure. “4-3” is not more “1” than 2/2 - both “code for” the same thing. So it is with all humans and future AGI: we will all share this same ability to be universal learners, or knowledge creators or problem solvers. Call it what you like. The code will be equivalent. Which is to say the software has the same capacity. A capacity for universality. That the code (the software) will be equivalent (thought it's unlikely of course to be identical in humans and AGI) it cannot be the case that intelligence is purely a matter of genetics. After all: AGI won't have genes.
What can, however, be different between two humans or humans and AGI are two bits of hardware that might, between people, be heritable: speed (of our processors) and/or memory. Both of these are, of course, improvable. But the software cannot have its capacity improved. If it’s universal, it’s universal. It can solve any problem. You can’t, in principle solve more problems than all the physically solvable problems that there are given enough resources (like matter, energy and time). So why don’t we solve all those problems or even attempt to? Well at the level of civilisation we simply don’t know about all the problems or have the resources. But as individuals it’s usually simply a mundane lack of interest. So is there a genetic component to intelligence? Yes: in that so far the only code we know for intelligence is written into the genes. We don’t know what it is. When we do, and when we can decode the genetic code for intelligence we will be able to code (perhaps far more efficiently) that code into AGI. Or maybe we’ll discover-using our creativity - a program for creativity before this. But it must be logically equivalent to the code in the DNA. But there can’t be “degrees” of intelligence of the kind we and AGI will have anymore than there are “degrees” of “oneness”. 2/2 and 4-3 and 1 all have precisely the same amount of “1” - namely a complete difference from 0 and 2 and all the other numbers that don’t have that at all.
IQ tests are said to be tests of intelligence. But they cannot be, unless one argues that "intelligence" is something like "interest in doing the kind of tasks associated with success in IQ tests". So, for example: doing lots of practise IQ test type questions would be one such task. So would mathematics and logic and reading lots of books. But none of this implies greater intelligence. It implies more knowledge, sure: knowing how. But not intelligence. Real intelligence should be regarded as the capacity (in principle) to creatively solve problems not before encountered. And this will depend in part on (1) how interested one is in attempting to solve such a problem (2) one's memory and (3) one's processing speed.
So call IQ tests a test of intelligence if you like but recognise it's like calling the results of your "height and weight" test a test of your beauty. Sure, there's possibly a relationship. Sure those results are correlated with all sorts of other things. But to say the test is truly, actually, a test of that phenomena is to ignore the simple fact you've arbitrarily named and therefore narrowly restricted a word with lots and lots of history and social baggage and generality. So call the people with high IQ "more intelligent" and call the tall people with low weight "more beautiful" but then appreciate: we're all equally intelligent in the most important way (we're universal) and we're all equally beautiful in the most important way too. And that should matter far more than measuring (then judging) people with numbers ascribed by psychologists.