The generator matrix

 1  0  0  0  0  0  1  1  1
 0  1  0  0  0  0  3  0  2
 0  0  1  0  0  0  1  2  2
 0  0  0  1  0  0  1  2  0
 0  0  0  0  1  0  1  1  3
 0  0  0  0  0  1  1  3  3

generates a code of length 9 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+113x^4+546x^6+1393x^8+1372x^10+567x^12+98x^14+6x^16

The gray image is a code over GF(2) with n=18, k=12 and d=4.
This code was found by Heurico 1.16 in 0.0296 seconds.