The generator matrix

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

generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+166x^12+192x^14+143x^16+10x^20

The gray image is a linear code over GF(2) with n=56, k=9 and d=24.
As d=24 is an upper bound for linear (56,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9.
This code was found by Heurico 1.16 in 0.00298 seconds.