The generator matrix

 1  0  0  0  1  1  1  X  1  1  1
 0  1  0  0  X  1  1  1 X+1 X+1  0
 0  0  1  0 X+1  1  X X+1  1 X+1  0
 0  0  0  1  1  X X+1  1  1 X+1  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+45x^8+66x^9+19x^10+18x^12+60x^13+42x^14+2x^17+3x^18

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 0.00143 seconds.