The generator matrix

 1  1  1  1  2  2  2  1  1  2  1  1
 0  2  0 14  6  6  0  0  0  0  0  0
 0  0 12  4  0 12 12  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+76x^4+264x^6+855x^8+128x^9+2936x^10+3968x^11+16312x^12+3968x^13+2936x^14+128x^15+855x^16+264x^18+76x^20+1x^24

The gray image is a code over GF(2) with n=96, k=15 and d=16.
This code was found by Heurico 1.16 in 0.247 seconds.