The generator matrix

 1  0  0  0  1  1  1  0  1  1  1
 0  1  0  0  0  1  1  1  X  X  0
 0  0  1  0  1  1  0  1  0  X  X
 0  0  0  1  1  0  1  1  1 X+1  1
 0  0  0  0  X  0  0  X  0  0  X
 0  0  0  0  0  X  0  X  X  X  X
 0  0  0  0  0  0  X  X  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+84x^6+64x^7+114x^8+256x^9+316x^10+384x^11+312x^12+256x^13+108x^14+64x^15+85x^16+4x^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 0.313 seconds.