The generator matrix

 1  0  0  1  1  1  0  1  1  1  1
 0  1  0  1  0  1  1  0  0  X  0
 0  0  1  1  1  0  1  0  X  X  0
 0  0  0  X  0  0  0  X  X  X  0
 0  0  0  0  X  0  0  X  X  0  0
 0  0  0  0  0  X  0  X  0  X  0
 0  0  0  0  0  0  X  X  X  X  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+42x^6+150x^8+310x^10+336x^12+150x^14+25x^16+10x^18

The gray image is a linear code over GF(2) with n=22, k=10 and d=6.
This code was found by Heurico 1.16 in 0.00364 seconds.