The first movie says.
How would he give himself access though? Zod is dead, and Kelor just says hello how can I help you when Lex walks in.
Forgive me if I remember incorrectly, but Zod never accessed the ship. He erased Jor-El from his ship, the Black Zero, but this ship is the one Clark found in the ice. (And then left for the government to keep for some reason.) I could be wrong though, will need to re-watch MoS.
He left the Black Zero and went to the scout ship because it had a birthing chamber on board, there he encountered Jor-El and proceeded to erase him from the system. Zod then flew the ship back to Metropolis where he attempted to stop the attack on the Black Zero that eventually sent the other Kryptonians back to the Phantom Zone.