The generator matrix

 1  1  1  1  2  1  1  1  1  2  1  1
 0 12  0  0 12  0  4 12  0  0  0  0
 0  0 12  0 12  4  4 12 12  0  0  0
 0  0  0 12 12  4  0 12  0  0  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+304x^6+1031x^8+1616x^10+2048x^11+22616x^12+2048x^13+1616x^14+1031x^16+304x^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 0.323 seconds.