[Base 4, aka quaternary] is an order of magnitude of greater complexity than Binary math (something for which we don't see forming except with Intelligent Intervention). Not really. The inherent mathematical complexity is largely the same, in any base. Humans use base 10 as a notational convenience, no doubt influenced by the specifics of anatomy. Lacking pinkies, we would likely count in octal.
While not mathematically more complex, base 4 does have the advantage that it requires only half the digits as binary (e.g. 255 decimal == 11111111 binary == 3333 quaternary).
Humans are well past the early computational barbarism of programming in straight binary (or assembly for that matter, except where required in performance critical applications). High-level languages and compilers ease the painstakingly precise drudgery of transforming high-level code into machine code. It is straightforward to modify a compiler back-end or assembler to emit low-level machine instructions in quaternary instead of binary. Thus, the mere fact of base 4 as the basis of DNA computation is not conclusive proof of anything, although it is an elegant bit of engineering.
Moreover, the dominance of binary in human machine computing, while a current fact, is not the last word. Advances in quantum computing will inevitably yield architectures with qubits (quantum bits) having bases greater than 2.
You raise some interesting points, however, and in doing so expose the late Asimov's myopia. Asimov laughably failed to deal with the obvious, namely the "big bang" postulated some 15 billion years ago, and from which the full vastness of the universe is theorized to have emanated from an infintesimally small point. The question at the limit, of course, is "Caused by Whom, and Why?"
Try as we might, and with all the hubris for which humans are famous, realize this. We are as two-year olds trying to understand quantum physics. God exists, but it is pure foolishness for us to think we can understand all He knows. In time, if we survive long enough, we may travel to the stars. It bears reminding who made the stars, not to mention the universe that contains them.
The question at the limit, of course, is "Caused by Whom, and Why?" Begs the Question there was a 'Whom' but the point is well made. Read Hawkins recently and he said we can't concern ourselves with what happened before the BANG! because there were no rules, no natural laws, no time, no anything before that so it didn't exist! Oh, that explains things.
I like to put thus, "What went Bang!?"
You may assume God exists if you wish but it is all the same. Nobody really knows. That's the one thought nobody wants to accept.
"[Base 4, aka quaternary] is an order of magnitude of greater complexity than Binary math (something for which we don't see forming except with Intelligent Intervention). Not really. The inherent mathematical complexity is largely the same, in any base. Humans use base 10 as a notational convenience, no doubt influenced by the specifics of anatomy. Lacking pinkies, we would likely count in octal. While not mathematically more complex, base 4 does have the advantage that it requires only half the digits as binary (e.g. 255 decimal == 11111111 binary == 3333 quaternary)." 
While I'm sure that you mean well, Base 4 IS literally an order of magnitude greater in complexity than Base 2.
0 , 1 vs 0, 1, 2, 3
In Binary you'd represent Base 2 as 10, while Base 4 would be 100.
100 is a single order of magnitude larger than 10, FYI...
But no matter. My point is that NEITHER Base 2 nor Base 4 software programs have ever been shown to have been formed by natural, unintelligent processes.
On the other hand, BOTH Base 2 as well as Base 4 software programs have been shown to have been formed EXCLUSIVELY by intelligent intervention (e.g. Man in the case of computer software).