The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^4+248x^6+384x^7+750x^8+5376x^9+624x^10+384x^11+332x^12+24x^14+9x^16

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 0.026 seconds.