The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+112x^4+168x^5+600x^6+1208x^7+2630x^8+3912x^9+4840x^10+5784x^11+4900x^12+3960x^13+2536x^14+1192x^15+673x^16+152x^17+88x^18+8x^19+4x^20

The gray image is a code over GF(2) with n=22, k=15 and d=4.
This code was found by Heurico 1.10 in 0.0493 seconds.