If you were permanently banned, then it wasn't for a single game. Unless your behavior is incredibly severe, it generally takes multiple games of bad behavior to be punished. The current system issues punishments in 4 tiers:
1.) 10 game chat restriction
2.) 25 game chat restriction
3.) 14 day ban
4.) Permanent ban
Your first punishment will be the first tier, and each punishment after that will move you up one tier, regardless of how "minor" the offense may have been. This means that any behavior that can get you a chat restriction can also get you a permanent ban if you do it frequently enough. It is possible to skip the chat restrictions and be escalated straight to a 14 day/permanent ban, but this only happens when Riot finds your behavior to be particularly extreme.
Something else to keep in mind is that the chat logs you receive aren't necessarily the only games that lead to your punishment. The system is only designed to send you chat logs of 1-3 games, and hey are simply examples of the behavior you exhibited that got you punished. They aren't an extensive list of everything you did to get punished.
Now, if you'd like to discuss your punishment here, I'd recommend posting all of the chat logs you received and I or someone else could go over them with you and point out what lead to the punishment. If you'd like to contest your punishment directly with Riot, the best way to do so would be to submit a support ticket.
If you haven't received a 14 day ban, or really any other punishment before this, it might be possible to get your punishment lowered to a 14 day ban. However, if you have received a 14 day ban recently, then it's very unlikely to get this punishment reversed, as a permanent ban is a standard next punishment after a 14 day ban.
