The generator matrix

 1  1  1  1  2  2  2  1  1
 0  2  0  6  6  6  0  0  0
 0  0 12  0  0  0 12  4  4
 0  0  0 12  0 12  0  4  4
 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+132x^4+992x^6+1280x^7+7102x^8+13824x^9+6976x^10+1280x^11+1076x^12+96x^14+9x^16

The gray image is a code over GF(2) with n=72, k=15 and d=16.
This code was found by Heurico 1.16 in 0.32 seconds.