The generator matrix

 1  0  0  0  0  1  1  1  1
 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  0

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

Homogenous weight enumerator: w(x)=1x^0+47x^2+302x^4+80x^5+722x^6+960x^7+976x^8+2016x^9+976x^10+960x^11+722x^12+80x^13+302x^14+47x^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 0.0566 seconds.