The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+164x^4+1024x^6+1024x^7+7038x^8+14336x^9+6912x^10+1024x^11+1108x^12+128x^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 0.326 seconds.