The generator matrix

 1  0  1  1  1  0  1  1  1
 0  1  1  0  1  1  0  0  0
 0  0  2  0  0  0  0  2  0
 0  0  0  2  0  0  0  2  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+29x^4+31x^6+64x^7+67x^8+128x^9+67x^10+64x^11+31x^12+29x^14+1x^18

The gray image is a code over GF(2) with n=18, k=9 and d=4.
This code was found by Heurico 1.16 in 0.00102 seconds.