The generator matrix

 1  0  0  0  1  1  1  6  1
 0  1  0  0  2  5  7  1  0
 0  0  1  0  3  1  2  3  0
 0  0  0  1  1  2  3  3  0

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

Homogenous weight enumerator: w(x)=1x^0+252x^5+1134x^6+4256x^7+13713x^8+26824x^9+13713x^10+4256x^11+1134x^12+252x^13+1x^18

The gray image is a code over GF(2) with n=72, k=16 and d=20.
This code was found by Heurico 1.16 in 2.05 seconds.