I'm pretty much with zook on this one. I think a minraise looks very scary here, plus it lets anyone with a set draw to their boat cheaply, especially if the SB for some reason calls. Any other raise will leave me obviously committed and as such look like I want to keep someone in. I think a push could look like the Ad or a set trying to push people off.

Here is how it went, my guess is that the BB laid down 99/88.

Flop: ($12) 9, Q, 8 (6 players)
SB bets $6, BB raises to $37, UTG folds, MP1 folds, MP3 folds, Hero calls $195 (All-In), SB calls $77.95 (All-In), BB folds.

Turn: ($327.95) 4 (2 players, 2 all-in)

River: ($327.95) A (2 players, 2 all-in)

Final Pot: $327.95

Results in white below:
SB has 7d Td (flush, ace high).
Hero has 3d Kd (flush, ace high).
Outcome: Hero wins $327.95.