The generator matrix

 1  1
 0 X+1

generates a code of length 2 over Z2[X]/(X^3) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+12x^1+38x^2+12x^3+1x^4

The gray image is a linear code over GF(2) with n=8, k=6 and d=2.
As d=2 is an upper bound for linear (8,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.712 seconds.