Beoro,
I am the Mod that banned you. Let me start by quoting from our rules:

Any form of cheating will not be tolerated - This means anything that gives you an unfair advantage over players who are playing the game the way the game was intended to be played. This includes but is not limited to: non-approved clients (hacked clients, minimaps), abusing in-game glitchs (duping, 0-tick farms, x-ray, breaking bedrock) and xray texture packs.

I understand that you claim to have been only getting some coal and diamonds. However, I have never seen someone so psychic as to be able to walk or run a path, come to a dead stop, turn and mine diamonds 3-6 walls deep, 3-4 levels up or down. You were witnessed doing this several times only where there were diamonds. It's not coincidence.
The offense you have committed comes with a lifetime ban as punishment.
I wish you well on another server, however this appeal is irrevocably denied.
~Ota