Numerology of Specified Complexity?

Stephen Pinker, Words and Rules, pp. 8-9

"Billions of years ago life on Earth settled on a code in which a string of three bases in a DNA molecule became the instruction for selecting one amino acid when assembling a protein. There are four kinds of bases, so a three-string base allows for 4 x 4 x 4 = 64 possibilites. That is enough to give each of the amino acids [20 of them] its own string, with plenty left over to start and stop instructions that begin and end the protein. two bases would have been too few (4 x 4 = 160, and four more than needed (4 x 4 x 4 x 4 = 256)."