The generator matrix

 1  1  X
 0  X X^2+X
 0  0 X^2

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

Homogenous weight enumerator: w(x)=1x^0+23x^2+16x^3+23x^4+1x^6

The gray image is a linear code over GF(2) with n=12, k=6 and d=4.
As d=4 is an upper bound for linear (12,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 3.19e-005 seconds.