Flopped 4 of a kind, did I max my money?

[bilbo-san]

Well, another question is whether or not calling 2 bets PF with 44 is a good call or not. The table seemed pretty loose and there had been a lot of cold calling so I thought the button and the blinds might also call. My plan is obviously flopping a set or folding so maybe this is a loose call.

Party Poker 1/2 Hold'em (10 handed)

Preflop: Hero is CO with 4[img]/images/graemlins/spade.gif[/img], 4[img]/images/graemlins/club.gif[/img].
UTG folds, UTG+1 folds, UTG+2 calls, MP1 folds, MP2 folds, MP3 raises, Hero calls, Button folds, SB folds, BB calls, UTG+2 calls.


Flop: (8.50 SB) J[img]/images/graemlins/club.gif[/img], 4[img]/images/graemlins/heart.gif[/img], 4[img]/images/graemlins/diamond.gif[/img] <font color="blue">(4 players)</font>
BB checks, UTG+2 checks, MP3 bets, Hero calls, BB folds, UTG+2 calls.

Obviously my only concern is maxing my money.

Turn: (5.75 BB) 2[img]/images/graemlins/club.gif[/img] <font color="blue">(3 players)</font>
UTG+2 checks, MP3 bets, Hero calls, UTG+2 folds.

I was worried (justifiably, it turned out) UTG+2 would fold to a raise, but should I raise anyway?

River: (7.75 BB) A[img]/images/graemlins/club.gif[/img] <font color="blue">(2 players)</font>
MP3 bets, Hero raises, MP3 calls.

Obviously would have been nice if this card gave MP3 a good flush, but that's probably what HE feared.

Final Pot: 11.75 BB