The generator matrix

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

generates a code of length 5 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+17x^2+24x^3+46x^4+80x^5+46x^6+24x^7+17x^8+1x^10

The gray image is a linear code over GF(2) with n=10, k=8 and d=2.
As d=2 is an upper bound for linear (10,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in 0.000119 seconds.