The generator matrix

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

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+26x^24+32x^25+36x^26+48x^27+22x^28+24x^29+16x^30+16x^31+13x^32+4x^34+2x^36+8x^37+8x^38

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 0.00575 seconds.