Well, to start off with, I'll be blunt; no, it's not possible for you to be unbanned. You were warned with the 14-day ban that further misbehavior would result in a permanent suspension. On top of that, Riot does not, as a general rule, overturn punishments that were not issued in error.
Beyond that, there's some more stuff that aught to be addressed, first and foremost being the deal of "scapegoating" and people ganging up on you. To start with the most common deal, group reports have no greater weight than singular reports - so if four people start harassing you and ultimately report you, the only reason you would be punished is if you decided to flame back.
If you had simply muted them and played the game to the best of your ability, their reports would have no effect. Stooping to their level and retaliating helps no one, and only serves to set you up to be punished.
So all of them decide to report me for speaking the truth.
However, my statement about them being awful people still stands.
I see the phrase "speaking the truth" bandied about a lot when the truth involved is beaten over someone's head. Seldom do I see people talking about "speaking the truth" when the truth isn't used to harass.
This unapologetic approach to your behavior doesn't really help with your desire to be unbanned. While it's a day late and a dollar short, you should still try to understand your punishment better.
I have to admit I used some offensive language but they were being just as toxic as me.
And, lastly, other people's toxicity does not excuse one's own. Sure, they may have been awful, deplorable trolls, but they don't control your actions. They were toxic - and, to turn your phrasing and try to give a better understanding here - you were just as toxic as them.
The IFS doesn't care about the details of toxicity - it doesn't care who started it, who retaliated, who was worse, etc. - it only cares that a reported player was toxic.
Hate to be the bearer of bad news, but, yeah. This is a case where getting unbanned isn't really gonna happen.
