The generator matrix

 1  0  0  1  1  1  1  1  1
 0  1  0  1  2  3  0  3  0
 0  0  1  1  1  0  2  3  0
 0  0  0  2  0  2  2  0  0

generates a code of length 9 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+18x^6+20x^7+13x^8+28x^9+16x^10+12x^11+10x^12+4x^13+6x^14

The gray image is a code over GF(2) with n=18, k=7 and d=6.
This code was found by Heurico 1.16 in 0.000377 seconds.