Chewy loves to run out the door. Luckily I am in an apt. building, but he could run down the stairs and hurt himself

What I have started doing is the stay command and showing him my palm straight in his face so that he corresponds the command with the action. It's only been a week or 2 but he IS learning. I would say that and the combination of the mat Kathy spoke of would be ideal.
Good luck with little Enzo and remember he is still so young. He will learn and get used to your commands and routine.