One attempt at a reroll, coming right up...

(4d6)[2][4][2][3](11)
(4d6)[2][5][1][2](10)
(4d6)[3][5][1][3](12)
(4d6)[2][4][1][3](10)
(4d6)[1][3][2][3](9)
(4d6)[3][1][4][1](9)

Pre-re-rolled ones:
(4d6)[1][6][3][5](15)
(4d6)[2][2][5][1](10)