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

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

Homogenous weight enumerator: w(x)=1x^0+67x^2+610x^4+2366x^6+5148x^8+5148x^10+2366x^12+610x^14+67x^16+1x^18

The gray image is a code over GF(2) with n=18, k=14 and d=2.
This code was found by Heurico 1.16 in 0.395 seconds.