Riot does not give a set timeline. They watch your game behavior and then decide when to lift your punishment.
People have gotten like 2 week bans then don't play for a month and then come back and say it's not fair that they can't get loot even though they stopped playing for a month. Their model is about showing whether or not you have reformed or want to even reform. If you don't play games, they can't see whether or not you want to reform/trying to reform and if you don't play games, they definitely can't see if you actually have reformed.
My advice to you is play sportsmanlike consistently and play games as frequently as you normally did before your punishment.