The generator matrix

 1  0  1
 0  1 X^2
 0  0  X

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

Homogenous weight enumerator: w(x)=1x^0+10x^1+47x^2+140x^3+47x^4+10x^5+1x^6

The gray image is a linear code over GF(2) with n=12, k=8 and d=2.
As d=3 is an upper bound for linear (12,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.000111 seconds.