The generator matrix

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

generates a code of length 11 over Z4 who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+12x^9+18x^10+12x^11+6x^12+4x^13+6x^14+4x^15+1x^16

The gray image is a code over GF(2) with n=22, k=6 and d=9.
This code was found by Heurico 1.16 in 0.000308 seconds.