The generator matrix

 1  0  1
 0  1 X+1
 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+39x^2+48x^3+39x^4+1x^6

The gray image is a linear code over GF(2) with n=12, k=7 and d=4.
As d=4 is an upper bound for linear (12,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7.
This code was found by Heurico 1.16 in 2.88e-005 seconds.