The generator matrix

 1  1  1  1  1  1  2  1  1
 0 12  0  0  0  0  4  8  0
 0  0 12  0  0  0  4 12  8
 0  0  0 12  0  4  0  4  8
 0  0  0  0 12  4  0  8  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+46x^4+52x^5+142x^6+240x^7+830x^8+5560x^9+844x^10+240x^11+142x^12+52x^13+38x^14+5x^16

The gray image is a code over GF(2) with n=72, k=13 and d=16.
This code was found by Heurico 1.16 in 0.0191 seconds.