The generator matrix

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

generates a code of length 4 over Z2[X]/(X^2) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+8x^1+28x^2+56x^3+70x^4+56x^5+28x^6+8x^7+1x^8

The gray image is a linear code over GF(2) with n=8, k=8 and d=1.
As d=1 is an upper bound for linear (8,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in 7.39e-005 seconds.