The generator matrix

 1  0  1  1  1  1  1  0  1  1  X
 0  1  1  0  1  0  0  1  0  X  X
 0  0  X  0  0  0  X  X  0  X  0
 0  0  0  X  0  0  X  0  0  X  X
 0  0  0  0  X  0  X  X  X  0  0
 0  0  0  0  0  X  X  0  X  X  0

generates a code of length 11 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+66x^8+48x^10+104x^12+16x^14+21x^16

The gray image is a linear code over GF(2) with n=22, k=8 and d=8.
As d=8 is an upper bound for linear (22,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in 0.0404 seconds.