The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+114x^4+540x^6+1408x^8+1352x^10+582x^12+92x^14+7x^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 0.0287 seconds.