The generator matrix

1 0 0 0 0 0 1 0 1 1 1
0 1 0 0 0 0 0 1 1 1 0
0 0 1 0 0 0 0 1 2 0 0
0 0 0 1 0 0 1 0 0 2 0
0 0 0 0 1 0 1 0 2 0 0
0 0 0 0 0 1 1 0 3 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+51x^4+32x^5+286x^6+256x^7+741x^8+992x^9+969x^10+1536x^11+969x^12+992x^13+741x^14+256x^15+286x^16+32x^17+51x^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 1.10 in 0.00977 seconds.