The generator matrix

1 0 0 0 0 1 1 1 1 1 1
0 1 0 0 0 1 0 1 X X+1 0
0 0 1 0 0 1 0 X 1 1 X+1
0 0 0 1 0 1 0 X+1 X+1 0 X
0 0 0 0 1 1 X+1 1 0 X 1
0 0 0 0 0 X X 0 X 0 0

generates a code of length 11 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+54x^6+104x^7+139x^8+232x^9+328x^10+336x^11+295x^12+272x^13+158x^14+72x^15+44x^16+8x^17+4x^18+1x^20

The gray image is a linear code over GF(2) with n=22, k=11 and d=6.
This code was found by Heurico 1.10 in 0.015 seconds.