The generator matrix

 1  1  1  1  1  1  1  X  1  1  1
 0  X  0  0  0  0  0  0  X  X  0
 0  0  X  0  0  0  0  X  X  X  0
 0  0  0  X  0  0  0  X  0  X  0
 0  0  0  0  X  0  0  X  0  X  X
 0  0  0  0  0  X  0  X  X  0  X
 0  0  0  0  0  0  X  X  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+13x^6+25x^8+89x^10+91x^12+23x^14+10x^16+3x^18+1x^20

The gray image is a linear code over GF(2) with n=22, k=8 and d=6.
This code was found by Heurico 1.16 in -5.72e-009 seconds.