The generator matrix

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

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+126x^12+96x^13+144x^14+95x^16+32x^17+16x^18+2x^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 1.11 in 0.016 seconds.