The generator matrix

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

generates a code of length 6 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+57x^4+114x^5+173x^6+108x^7+54x^8+2x^9+3x^10

The gray image is a linear code over GF(2) with n=24, k=9 and d=8.
As d=8 is an upper bound for linear (24,9,2)-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.