A short (and not entirely correct) answer is: *redundancy*.  There is a very nice article on this in Barry Hayes book, *[Group Theory in the Bedroom][1]*.  The precursor of the chapter appeared in the *American Scientist*:
"[The Invention of the Genetic Code][2]".  One interesting aspect of the story is that George Gamov
proposed several clever triplet genetic codes of great abstract beauty.  Other physicists and mathematicians (Feynman, Teller, Golomob) also made suggestions.  But nature chose its own path.


  [1]: http://www.amazon.com/Group-Theory-Bedroom-Mathematical-Diversions/dp/0809052199
  [2]: http://www.americanscientist.org/issues/pub/the-invention-of-the-genetic-code