Design an experiment in which random, agitated matter inside a container is observed over time.
Now ask yourself, for this experiment, is it equally likely, more likely, or less likely that I witness "order" spontaneously (and without intelligent intervention of any sort) form from this chaos in which a two item pattern (e.g. 0,1) emerges in contrast to a four item pattern (e.g. 0,1,2,3) emerging?
I think that you'll eventually agree that the two-item pattern is an order of magnitude more likely to form.
The number base used for DNA computation, while extremely interesting, is not crucial to the issue of intelligent creation, although base 4 computation does have some advantages for a biological organism; it combines flexibility with relative simplicity. It would be no less amazing if there had been two or eight DNA bases instead of four. The issue is not the number base (not to be confused with DNA base ;), but that such sophisticated computation occurs at all.
The real complexity lies in the software, not the number base in which it is represented. One can write both extremely complex and extremely trivial programs, regardless of the base used to represent the instructions and data. Fruit flies share the same four DNA bases with humans, and have many similarities at the protein level.
If long-term survival is the metric, it's not even clear that humans have better software than fruit flies, taken as a species. If we continue down the path we're on, we might soon face the evolutionary equivalent of the Blue Screen of Death.
Without God, that is exactly what will happen.