You want to ask yourself these honest questions.
1. Are you actually open to other people's opinions? Or do you have your mind already set that you are "innocent" and no matter what people say, you will just be out trying to prove to them how you were treated unfairly. If that's the case, you are wasting your time posting, because we are honestly trying to help you out and give you quality advice on how to improve your behaviors. Listen to us and you probably won't be banned again.
2. Have you looked over your case and did you spot any sarcasm, negativity, non-constructive comments, trying to upset others, spamming in chat, raging, insults towards others, and other such "toxic" behaviors? If so, these should be pretty obvious behaviors that provide nothing constructive towards the game. It's pretty simple, you should stop doing any of these said behaviors.
3. Are you willing to try to alter your behaviors, even if you still feel that you have been wrongfully punished? This is what makes a good human being. Being able to try to see from other people's opinions (as equal to yours). Sometimes, we can be blinded by biases, which another person's point of view can be extremely helpful. Trying to be understanding of others can definitely help your overall behaviors in LoL.
4. Are you going to recognize your behaviors in game (and yours alone)? Or are you going to try to make excuses as to why you behaved the way you did? Remember, you can give reasons for your behaviors, but they never excuse them. The only person that you can control is yourself. It doesn't matter what they did. It only matter what you have done.
5. Are you wondering how to change your behaviors? If that's the case, maybe you already know the areas that you could improve upon. Maybe you already know your weaknesses and vulnerabilities. It might help you to think about life outside of League of Legends and notice ways that you might be "taking out" some of your frustrations on the battlefields. Sometimes things can get tense and if you had a rough day.....then maybe you shouldn't play Leagues. If you are on a losing streak, take a break for a while. If you would like some more helpful coping skills then feel free to ask!
I hope this is a helpful start towards your progress in becoming a positive summoner on the battle fields. Use the opportunities on this forums to grow as a person and become someone that everyone want to play a game with.
Lastly, please post your reform card (if you have one). The reform card is there to provide us with insight into your case (or cases). This is very important to us to see to provide you with our opinions into your case.