The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+145x^4+96x^5+1410x^6+4352x^7+13809x^8+25920x^9+13788x^10+4352x^11+1431x^12+96x^13+130x^14+6x^16

The gray image is a code over GF(2) with n=72, k=16 and d=16.
This code was found by Heurico 1.16 in 0.938 seconds.