The generator matrix

 1  1  1  1  2  2  2  1  1  2  1  1
 0 12  0  4  0  4 12  0  0  0  0  0
 0  0 12  4 12  4  0  0  0  0  0  0
 0  0  0  8  0  0  0  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  0  0
 0  0  0  0  0  8  0  0  0  8  0  0
 0  0  0  0  0  0  8  0  0  8  0  0
 0  0  0  0  0  0  0  8  0  8  0  0
 0  0  0  0  0  0  0  0  8  8  0  0

generates a code of length 12 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+60x^4+120x^6+503x^8+1544x^10+11928x^12+1544x^14+503x^16+120x^18+60x^20+1x^24

The gray image is a code over GF(2) with n=96, k=14 and d=16.
This code was found by Heurico 1.16 in 0.0843 seconds.