The generator matrix

 1  0  1  1  1  0  1  1  0  1  1
 0  1  1  0  1  1  0 X+1  1  0  0
 0  0  X  0  0  0  0  X  0  0  X
 0  0  0  X  0  0  0  X  0  X  X
 0  0  0  0  X  0  0  X  X  X  0
 0  0  0  0  0  X  0  X  X  0  0
 0  0  0  0  0  0  X  X  0  X  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+16x^6+78x^8+164x^10+160x^12+72x^14+17x^16+4x^18

The gray image is a linear code over GF(2) with n=22, k=9 and d=6.
This code was found by Heurico 1.16 in 6.87e-008 seconds.