So Eugene did say it once as shown (https://xenogamers.com/rank/player_histories/chat/94550), and that's it. He has never been punished in anyway for slurs before so jumping to a ban is not something that should be acceptable. The way I see it should be, and similar situations in the past have been, handled is that he should be contacted directly by staff in some manner and given a clear cut warning about it. Then the next time he breaks the rule he should receive a slightly more severe punishment then normal, but since it would still be his first punishment for slurs it should just be a longer mute at most. That is assuming he hasn't been warned by a staff member before for this in which case he should just receive the mute. This would all be much less convoluted had this just been done as a calladmin but not much can be done about that now.
Then there is Brian at the end there. This report isn't directed at him at all, yet he did the much more condemning offense. Looking at his history (https://bans.xenogamers.com/index.php?p=banlist&advSearch=STEAM_0:1:242346823&advType=s)he has been banned before for slurs, though it was tied in with micspam and leaving to avoid punishment. Being itself a single incident that involved a different kind of issue and from some time ago (about 8 months) it's not exactly a good punishment to bridge from, but unlike Eugene he still has had punishment for this before and should probably receive more then just a warning (more so considering the manner in which it was done). At that, I'd say a day mute would be adequate for the situation here.
I also really like home you omitted your own comment relating to Brian from the screenshots, but had you omitted brains entire segment I, and probably anyone else, wouldn't have even noticed what he did.
-1 ban Eugene, warn him at most
+1 punish Brian, day mute