The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  1  0 X^2
 0  X  0  X  0 X^2 X^2+X X^2+X X^2  X X^2+X  0  X  X
 0  0  X  X  0  X X^2+X  0 X^2+X X^2+X X^2 X^2+X X^2 X^2+X
 0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  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+86x^12+96x^14+63x^16+10x^20

The gray image is a linear code over GF(2) with n=56, k=8 and d=24.
As d=24 is an upper bound for linear (56,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.0962 seconds.