The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+47x^4+50x^5+138x^6+250x^7+323x^8+420x^9+332x^10+260x^11+137x^12+42x^13+42x^14+2x^15+4x^16

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 0.00645 seconds.