So, I don't want to rain on anyone's parade, but we didn't "just" find this out. We've known for quite a long time about secondary (and even tertiary!) "codes" in DNA. That HN article was the result of a press-release about something that was interesting, but certainly not earth-shattering new theory. The reason it was in Science was because they did an extremely large-scale test of a whole bunch of different codons on thousands of different gene promoters, and directly quantified the impact of rare codons. That was an impressive way to settle an open debate.
Anyway, it's good to know that there are higher-order interactions encoded in DNA than just DNA -> RNA -> Protein, but you should realize that this is an old/deep area of research. This is pretty much what bioinformatics is about, actually: deducing the higher-order structures in DNA, RNA and proteins.
https://news.ycombinator.com/item?id=6896779
And then there's RNA, which can fold and form structures, sort of like proteins.
Anybody who has ever seriously dealt with things produced by evolution knows that evolution "cheats" and optimizes when constrained by resources, producing structure upon structure upon structure, crazy indirection and non-obvious side-effects, as long as it helps the goal (survival and reproduction usually).
That's why I don't think human brains will be understood any time soon. We might figure out all the layers, but to figure out all the hidden structures would take a superhuman AI.
EDIT:
Example of circuit design by evolutionary algorithms:
http://hforsten.com/evolutionary-algorithms-and-analog-elect...