Mission To Mars "password" entropy

In the movie Mission To Mars, the "Face on Mars" emits a communication to the astronauts which translates into 3D coordinates mapping out human DNA but with the last pair of chromosomes missing. The idea of this being that if humans ever found the communication, they could fill in the final pair of chromosomes as a sort of password.

However, each side (nucleotide) of a pair of chromosomes can only be adenine (A), cytosine (C), guanine (G) or thymine (T). Even without knowing how base pairs relate to each other, there are only 6 possible combinations for this password, (AC, AG, AT, CG, CT or GT) or 12 if the ordering matters. This is as secure as choosing a single letter lower-case password between "a" and "f" (or "a" and "l"). Not very secure.... silly martians.