The generator matrix

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

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+330x^8+616x^12+77x^16

The gray image is a linear code over GF(2) with n=22, k=10 and d=8.
As d=8 is an upper bound for linear (22,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.10 in 0.172 seconds.