The generator matrix

 1  1  1  1  1  1  1  1  2  2  2  1
 0  2  0  6  0  6 12 14  6  6  0  0
 0  0 12  0  0  4 12  4  0  8  0  0
 0  0  0 12 12  4 12  0  0  8  8  0
 0  0  0  0  8  0  0  8  0  8  8  0
 0  0  0  0  0  8  0  8  0  0  8  0
 0  0  0  0  0  0  8  8  8  8  8  0

generates a code of length 12 over Z16 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+55x^6+100x^7+131x^8+464x^9+1243x^10+1500x^11+9437x^12+1440x^13+1221x^14+508x^15+152x^16+80x^17+41x^18+4x^19+7x^20

The gray image is a code over GF(2) with n=96, k=14 and d=24.
This code was found by Heurico 1.16 in 0.12 seconds.