The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+50x^24+56x^26+75x^28+24x^30+22x^32+16x^34+9x^36+3x^40

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^2) for dimension 8.
This code was found by Heurico 1.16 in 0.00623 seconds.