The generator matrix

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

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+56x^6+92x^7+172x^8+216x^9+274x^10+392x^11+300x^12+256x^13+172x^14+60x^15+39x^16+8x^17+10x^18

The gray image is a linear code over GF(2) with n=22, k=11 and d=6.
This code was found by Heurico 1.16 in 0.0148 seconds.