The generator matrix

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

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+52x^2+96x^3+214x^4+96x^5+52x^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 1.16 in 0.000126 seconds.