The generator matrix

 1  1  1
 0  X 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+3x^2+24x^3+3x^4+1x^6

The gray image is a linear code over GF(2) with n=12, k=5 and d=4.
As d=4 is an upper bound for linear (12,5,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 5.
This code was found by Heurico 1.16 in 2.1e-005 seconds.