The generator matrix

 1  0  0  0  1  1  1  X  1  1  0  0  X  X  1  1  1  1  1  0  1  1  X  1  1  0  1  1
 0  1  0  0  X  X  X  0 X+1  1  1  1  1  1  1 X+1 X+1  0  0  1  0  1  1  X  0  X  1  0
 0  0  1  0  0 X+1  1  1  0  X  1 X+1  X  0  1  1  X  X  X  X  0 X+1 X+1  0  1  1  X  X
 0  0  0  1  1 X+1  0  1  X X+1 X+1  X  1  0  X X+1  1  X  0  1 X+1  0 X+1 X+1  X  X  1  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+32x^24+36x^25+25x^26+42x^27+26x^28+20x^29+18x^30+16x^31+11x^32+8x^33+7x^34+6x^35+2x^36+4x^38+2x^42

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 0.00529 seconds.