The generator matrix

 1  1  1  1  2  2  1  1  1
 0 12  0 12 12 12  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+31x^6+128x^7+67x^8+1536x^9+67x^10+128x^11+31x^12+29x^14+1x^18

The gray image is a code over GF(2) with n=72, k=11 and d=16.
This code was found by Heurico 1.16 in 0.00255 seconds.