My boyfriend wants me to sign a contract of things not to do

I was texting a guy who wasn't my boyfriend, and my boyfriend found out. We work together, so he went to work and told everyone I was cheating on him. I moved out of the house. There have been previous problems, and I feel like I'm usually the issue here. In order for us to move on, he wants me to sign this contract that he wrote out listing things he doesn't want me to do anymore. I'm wondering if this a healthy relationship to save or if I should walk away.