With a brute force program solver written in C#, I found a solution with sum 366:
3 11 5 | 19
37 17 13 | 67
7 31 23 | 61
---------+---
29 47 59 41 | 43
The program still runs, though, so there might be better solutions.
Source code at PasteBin (you might want to change the initial value of recordSum to something bigger than 366 to actually get some results).