The generator matrix

 1  0  0  1
 0  1  0  1
 0  0  1  1

generates a code of length 4 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+36x^2+96x^3+246x^4+96x^5+36x^6+1x^8

The gray image is a linear code over GF(2) with n=16, k=9 and d=4.
As d=4 is an upper bound for linear (16,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9.
This code was found by Heurico 1.11 in 6.87e-008 seconds.