The generator matrix

 1  1  1  1  1  1  1  1  1
 0  2  0  0  4 14 10 10  0
 0  0  2  0  6  6  6  4  0
 0  0  0  2  2  4  6  2  0

generates a code of length 9 over Z16 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+84x^5+182x^6+336x^7+1225x^8+4536x^9+1225x^10+336x^11+182x^12+84x^13+1x^18

The gray image is a code over GF(2) with n=72, k=13 and d=20.
This code was found by Heurico 1.16 in 0.0322 seconds.