The generator matrix

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

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+18x^1+111x^2+252x^3+111x^4+18x^5+1x^6

The gray image is a linear code over GF(2) with n=12, k=9 and d=2.
As d=2 is an upper bound for linear (12,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9.
This code was found by an older version of Heurico in 0 seconds.