The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+121x^4+48x^5+842x^6+1728x^7+6209x^8+14880x^9+6188x^10+1728x^11+863x^12+48x^13+106x^14+6x^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.