The generator matrix

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

generates a code of length 5 over Z2[X]/(X^2) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+10x^1+45x^2+120x^3+210x^4+252x^5+210x^6+120x^7+45x^8+10x^9+1x^10

The gray image is a linear code over GF(2) with n=10, k=10 and d=1.
As d=1 is an upper bound for linear (10,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by an older version of Heurico in 0 seconds.