The generator matrix

 1  0  0  0  0  0  1  1  1
 0  1  0  0  0  0  1  0  0
 0  0  1  0  0  0  1  0  0
 0  0  0  1  0  0  1  0  0
 0  0  0  0  1  0  1  0  0
 0  0  0  0  0  1  1  0  0
 0  0  0  0  0  0  2  0  0
 0  0  0  0  0  0  0  2  0
 0  0  0  0  0  0  0  0  2

generates a code of length 9 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+69x^2+792x^4+4368x^6+11154x^8+11154x^10+4368x^12+792x^14+69x^16+1x^18

The gray image is a code over GF(2) with n=18, k=15 and d=2.
This code was found by Heurico 1.16 in 0.79 seconds.