Why remake a game that's not your game? You can get in legal troubles. Make your own FPS with zombies, it's probably a similar amount of work. You don't even have to be really original, just copy some features of different games.
It's for learning purposes. Everything will be provided for free for users as well as the game. I liked the game and want to remake it, and provide tutorials along the way for anyone else who is interested.
Your intentions are good, but lawyers don't care about intentions. Companies are legally required to defend their trademarks, or they risk losing them, so if Activision's legal team were to find out about your remake, they wouldn't hesitate in telling you to remove it, no matter what your reasons for making it are.
All you need to do is change the game enough that it's different from the original (using your own assets, obviously) and call it a tutorial on making CoD: Zombies style games.
Thanks, Yeah hopefully making a few changes will be enough. This helps, appreciate it.