The generator matrix

 1  0  1  1  1  4  2  8  1
 0  1  1  0  3  1 14  0  0
 0  0  2  0  2  4  2  2  0
 0  0  0  2  2  6  6  4  0

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

Homogenous weight enumerator: w(x)=1x^0+108x^5+350x^6+1088x^7+4001x^8+5288x^9+4001x^10+1088x^11+350x^12+108x^13+1x^18

The gray image is a code over GF(2) with n=72, k=14 and d=20.
This code was found by Heurico 1.16 in 0.0933 seconds.