The generator matrix

 1  0  X  X  1  1  1  X  1  0  1  1  1  X  1  0  1  X  1  1  X  0  1  0  1  X  1  1
 0  1  X  X X+1  1  X  1  0  1 X+1  1  X  1  0  1  X  1 X+1  1  0  X  0  1  X  0 X+1  1

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+8x^29+4x^30+3x^32

The gray image is a linear code over GF(2) with n=56, k=4 and d=29.
As d=29 is an upper bound for linear (56,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.132 seconds.