The generator matrix

 1  0  0  0  1  0  X  0  1  1  X
 0  1  0  0  0  1  X  X X+1 X+1  0
 0  0  1  0  0  0  1  X  1 X+1  X
 0  0  0  1  0  X  0  1  1  1  X
 0  0  0  0  X  X  X  X  0  X  X

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+170x^8+296x^12+45x^16

The gray image is a linear code over GF(2) with n=22, k=9 and d=8.
As d=8 is an upper bound for linear (22,9,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 9.
This code was found by Heurico 1.16 in 2.38 seconds.