The generator matrix

 1  1  1  1  2  2  1  1  1  1  1  1
 0 12  0 12 12 12  0  0  0  0  0  0
 0  0  8  0  0  0  0  0  0  8  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+44x^4+40x^6+215x^8+600x^10+6392x^12+600x^14+215x^16+40x^18+44x^20+1x^24

The gray image is a code over GF(2) with n=96, k=13 and d=16.
This code was found by Heurico 1.16 in 0.0219 seconds.