The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+173x^6+160x^7+234x^8+384x^9+616x^10+960x^11+616x^12+384x^13+234x^14+160x^15+173x^16+1x^22

The gray image is a code over GF(2) with n=22, k=12 and d=6.
This code was found by Heurico 1.16 in 0.555 seconds.