The generator matrix

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

generates a code of length 8 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+65x^4+236x^6+419x^8+240x^10+59x^12+4x^14

The gray image is a linear code over GF(2) with n=16, k=10 and d=4.
As d=4 is an upper bound for linear (16,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.10 in 0 seconds.