The generator matrix

 1  1  1  1  1  1  1  1  1
 0  2  0  0  4 14 10  2  0
 0  0  2  0  6 14 14  0  0
 0  0  0  2  2 12 14  2  0
 0  0  0  0  8  0  0  8  0
 0  0  0  0  0  8  0  8  0
 0  0  0  0  0  0  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+109x^4+568x^5+1455x^6+3104x^7+7651x^8+39760x^9+7651x^10+3104x^11+1455x^12+568x^13+109x^14+1x^18

The gray image is a code over GF(2) with n=72, k=16 and d=16.
This code was found by Heurico 1.16 in 0.77 seconds.