The generator matrix

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

generates a code of length 11 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+43x^6+40x^7+96x^8+128x^9+116x^10+176x^11+116x^12+128x^13+96x^14+40x^15+43x^16+1x^22

The gray image is a code over GF(2) with n=22, k=10 and d=6.
This code was found by Heurico 1.16 in 0.0043 seconds.