The generator matrix

 1  1  1  1  2  1  1  1  1
 0  2  0  6  6  8  4  6  0
 0  0 12  0  0  8 12  4  0
 0  0  0 12  0 12  8  4  8
 0  0  0  0  8  0  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+30x^5+70x^6+170x^7+694x^8+2156x^9+708x^10+180x^11+56x^12+22x^13+6x^14+2x^15+1x^16

The gray image is a code over GF(2) with n=72, k=12 and d=20.
This code was found by Heurico 1.16 in 0.00887 seconds.