The generator matrix

 1  1  1  1  2  2  2  1  1
 0  2  0 14  6  6  8  0  0
 0  0 12  4  0 12  4  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  0

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

Homogenous weight enumerator: w(x)=1x^0+55x^4+192x^6+160x^7+781x^8+1728x^9+760x^10+160x^11+213x^12+40x^14+6x^16

The gray image is a code over GF(2) with n=72, k=12 and d=16.
This code was found by Heurico 1.16 in 0.00443 seconds.