Once they've learned to climb, it's pretty much over. They'll try to climb over anything you put them in. I even tried one of those soft play pen things with a cover. My boy ended up chewing through the fabric netting on the door. He was even able to climb over an extra tall baby gate with horizontal bars.
It might be better to leave him in a puppy proofed room with the door closed. That way, you won't have to worry about him injuring himself trying to make an escape attempt. Or a large crate. Good luck! I feel your pain