You were afk before that between;
[15:46:25] kill,Nomad,dagu807,melee,Red Tassel Spear,hb_calf_l
[15:49:46] msg,[ADMIN][Patoson] dont leech Frank
Given that the first kill there is the nomad, being close enough for you to kill, and that the first thing with nomads, where you DIE was at;
[15:49:55] kill,Frank_Of_Brack,Nomad,ranged,Tatar Bow,Tatar Arrows,hb_head
that clearly shows that you weren't participating in the battle.
The logs show that you weren't responding, the last record of you beforehand was you again, dying to the bots;
[15:44:33] kill,Frank_Of_Brack,Bandit,melee,Maul,hb_spine
So, this whole incident spans roughly 6 minutes, for which you show in the logs only four times, one of which is Patoson banning you, the other, warning you and the other two where you died, having done nothing else. I'm strongly inclined to say that you were leeching, you did not respond nor did you kill anything, no one is that bad at level 30 with teammates around you.
The bottom line is, you're leeching, the logs back that story up, and the ban was miniscule, you broke the rules and thus you deal with the consequences.