The generator matrix

 1  1  1  1  2  2  1  1  2
 0  2 12  6  6  6  0  0  0
 0  0  8  0  0  0  0  0  8
 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+44x^4+32x^5+104x^6+640x^7+910x^8+4800x^9+784x^10+640x^11+188x^12+32x^13+8x^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 0.0207 seconds.