The generator matrix

 1  0  0  0  1  1  1  1  1
 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  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+33x^2+220x^4+924x^6+2918x^8+2918x^10+924x^12+220x^14+33x^16+1x^18

The gray image is a code over GF(2) with n=18, k=13 and d=2.
This code was found by Heurico 1.16 in 0.0539 seconds.