The generator matrix

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

generates a code of length 11 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+22x^4+112x^5+199x^6+336x^7+664x^8+976x^9+1162x^10+1248x^11+1162x^12+976x^13+664x^14+336x^15+199x^16+112x^17+22x^18+1x^22

The gray image is a code over GF(2) with n=22, k=13 and d=4.
This code was found by Heurico 1.16 in 0.138 seconds.