The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+62x^26+26x^28+20x^30+3x^32+14x^34+2x^36

The gray image is a linear code over GF(2) with n=56, k=7 and d=26.
As d=26 is an upper bound for linear (56,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.0597 seconds.