The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+77x^4+56x^5+175x^6+224x^7+259x^8+464x^9+259x^10+224x^11+175x^12+56x^13+77x^14+1x^18

The gray image is a code over GF(2) with n=18, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00957 seconds.