The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+84x^6+64x^7+114x^8+256x^9+316x^10+384x^11+312x^12+256x^13+108x^14+64x^15+85x^16+4x^18

The gray image is a code over GF(2) with n=22, k=11 and d=6.
This code was found by Heurico 1.16 in 0.293 seconds.