Perhaps the 340 is meant to be folded up like the alien message from the movie Contact, sent from the Vegans.

Thinking Z must have been pretty tired after creating these codes so any folding would be on the simple side and why not in a "Z?"

So I just took a piece of paper, folded it in thirds and then took that and folded in thirds but in different directions on the end and it does form a "z" if you look at it on the side (easy to do, hard to explain).