The generator matrix

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

generates a code of length 9 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+42x^4+36x^5+90x^6+112x^7+374x^8+2776x^9+388x^10+112x^11+90x^12+36x^13+34x^14+5x^16

The gray image is a code over GF(2) with n=72, k=12 and d=16.
This code was found by Heurico 1.16 in 0.00763 seconds.