This shouldn't be affecting anything related to the server that would cause it to think that you're using a modified client. It looks like that you used something that gave you more minions than what was possible in vanilla.
You were not banned for "talking bad about Cy". The reason for the ban is for using an alt account on discord and spamming racial slurs. Then you continued to join on alt accounts trying to avoid the ban.
When you registered an account on the server it sent you the rules after you logged in. However, even if this wasn't the case it is the player's responsibility to know the general rules and guidelines of a server they play on.
Modified clients are not allowed as they can be harmful to the server as well as the experience of other players. Do you understand why this is the case?
Even if it was your brother that was spamming, you have responsibility for what happens on your account. Do you understand why this is the case and how what happened led to this punishment?