The generator matrix

 1  0  1  1  1  0  1  1  1
 0  1  3  6  5  1  0  0  0
 0  0  8  0  0  0  0  8  0
 0  0  0  8  0  0  0  8  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+29x^4+96x^5+31x^6+448x^7+1219x^8+4544x^9+1219x^10+448x^11+31x^12+96x^13+29x^14+1x^18

The gray image is a code over GF(2) with n=72, k=13 and d=16.
This code was found by Heurico 1.16 in 0.0132 seconds.