A solution for 4 idempotent MOLS(15) follows 
from a (14,6;1,0;1) QDM over Z_14. 
(This QDM also gives 2 SOLS(15).) 

The first 8 of the columns are:

   -  0  0  0   0  0  0  0
   1 10  8  2   6 12  9  1
   8  4  -  1  10  9 11  2
   0  1  2  3   4  5  6  7
   5 12  5  -  11  4 10  8
   3  7  1 11   2 10 13  9

Then for each given column  (a b c d e f)  (except the last)
we add one more, (d e f a b c).