KK with Double Paired Board

[CWsports]

I could use advice on how this hand should have been played.

Party Poker 0.50/1 Hold'em (10 handed) converter

Preflop: Hero is UTG+1 with K[img]/images/graemlins/spade.gif[/img], K[img]/images/graemlins/diamond.gif[/img].
<font color="CC3333">UTG raises</font>, <font color="CC3333">Hero 3-bets</font>, UTG+2 calls, MP1 folds, MP2 folds, MP3 folds, CO folds, Button folds, SB calls, BB folds, <font color="CC3333">UTG caps</font>, Hero calls, UTG+2 calls, SB calls.

Flop: (17 SB) J[img]/images/graemlins/club.gif[/img], J[img]/images/graemlins/spade.gif[/img], 4[img]/images/graemlins/heart.gif[/img] <font color="blue">(4 players)</font>
SB checks, <font color="CC3333">UTG bets</font>, <font color="CC3333">Hero raises</font>, <font color="CC3333">UTG+2 3-bets</font>, SB folds, UTG folds, Hero calls.

Turn: (12 BB) 4[img]/images/graemlins/spade.gif[/img] <font color="blue">(2 players)</font>
Hero checks, <font color="CC3333">UTG+2 bets</font>, Hero calls.

River: (14 BB) K[img]/images/graemlins/heart.gif[/img] <font color="blue">(2 players)</font>
Hero checks, <font color="CC3333">UTG+2 bets</font>, <font color="CC3333">Hero raises</font>, <font color="CC3333">UTG+2 3-bets</font>, <font color="CC3333">Hero caps</font>, UTG+2 calls.

Final Pot: 22 BB
<font color="green">Main Pot: 22 BB, between Hero and UTG+2.</font> &gt; <font color="white">Pot won by Hero (22 BB).</font>

Results in white below: <font color="white">
Hero has Ks Kd (full house, kings full of jacks).
UTG+2 has Qc Jd (full house, jacks full of fours).
Outcome: Hero wins 22 BB. </font>