20/40 flopping quads vs overpairs, extracting max value

[dark_horse]

semi-aggressive and semi-loose 7 handed 20/40 live game. i have a tight, solid, winning image. i have the big stack at the table. i am quiet and calm and my reads have been very strong throughout the session.

i am UTG with 88 and raise. a young hoodie (don't know much about his play) 3bets me, and another unknown player caps it. it's folded back to me, and i am almost certain at least one of them has an overpair to my eights, possibly both of them. although the table is aggressive, there isn't much capping preflop, but lots of 3betting. i seriously considered folding, but finally called because i knew i could make a huge pot if i flopped a set. plus i was getting 5:1. i called planning to dump my hand if i didn't improve.

the flop comes 882. how would you proceed?