I recommend focusing less on the time, and more on the behavior. If you correct the behavior, the time will take care of itself. That said, you do have to actually play to prove that you've reformed. Simply staying away from the game doesn't show them that you're behavior is any better. They need actual proof.
I don't know the details around the ban, but I'm assuming it was for chat behavior. Given that, here are a few general recommendations on what to do (and what not to do) once you're back from your 2-weeks to make sure you don't lose your account.
- Aim for neutral first. Riot doesn't expect players to go from 2-week bans to suddenly being top-tier examples of positive players. If you try to do this, you'll probably just stress yourself out which won't help your situation at all. All you have to do is not be negative, and they'll see you as improving. Keep this in mind for the rest of the points here.
- Impose a self-chat restriction. At the most extreme, just communicate solely through pings, and avoid spam pinging on top of allies to vent frustration with them. If you feel you can manage it, you could also give yourself a limited set of allowed phrases that you use in chat, and nothing else. These would be gameplay-related things like "dragon", "baron", "push x lane", or maybe even the occasional "gj" when allies get kills or objectives, or if your jungler gives a good gank.
- If your biggest issue is retaliation against other players when they start to go off in chat, be proactive towards avoiding that from the start. You could just get into the habit of doing a "/mute all" at the start of each game. Or else you could move the chat box so it's mostly off the screen so you can't see when allies are raging at you. If you think you can handle it to a certain point, perhaps you leave people unmuted at the start, but then be quick to mute them the moment you feel remotely compelled to respond.
- Make a habit of giving a cursory "GG" after the game. Some might feel it's a bit contrived, but it's still good sportsmanship and an easy way to get into that habit. And don't augment it with anything (no GG EZ), unless the other team had an AFK where a "sorry about the leaver" can be a nice, polite touch.
If you put these into practice, you should be able to avoid further punishments on your account. After all, the basic criteria for avoiding bans is "don't be a dick". Make a habit of these things and you'll be able to enjoy playing without fear of punishment for a long time.