Where did they get the ship?

Humans built them.

there's a few yadda-yadda moments in this story.. and I'm afraid this is one of 'em

Humans and AI fought a massive war. I assume most of the human survivors' tech like the electric "flamethrower" (lightning thrower?) and the hovercrafts are leftover weaponry from that. They squirreled away enough to survive with guerrilla tactics and then slowly grabbed enough stuff to construct Zion.

One of the things they probably do while flying around is look for more stuff to scavenge.