The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+172x^24+32x^28+51x^32

The gray image is a linear code over GF(2) with n=52, k=8 and d=24.
As d=24 is an upper bound for linear (52,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in 15.9 seconds.