The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+12x^14+1x^16+2x^20

The gray image is a linear code over GF(2) with n=56, k=4 and d=28.
As d=29 is an upper bound for linear (56,4,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 4.
This code was found by Heurico 1.16 in 0.000527 seconds.