The generator matrix

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

generates a code of length 9 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+113x^4+546x^6+2417x^8+10240x^9+2396x^10+567x^12+98x^14+6x^16

The gray image is a code over GF(2) with n=72, k=14 and d=16.
This code was found by Heurico 1.16 in 0.116 seconds.