The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  0  0  0  0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X
 0  X  0  0  0  X  X  X  0  0  0  X  0  X  X  X  0  0  0  X  X  0  0  X  0  X  X  X  X  X  X  0  0  0  0  X  X  X  0  0  0  X  0  X  X  X  0  0  0  0  X  X
 0  0  X  0  X  X  X  0  0  0  X  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  0  0  0  X  X  X  X  0  X  X  0  0  0  0  X  X  X  X  0  0  0  0  0  X  X  0
 0  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  0  0  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  0  X  X  0  0

generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+18x^52+8x^54+4x^56+1x^72

The gray image is a linear code over GF(2) with n=104, k=5 and d=52.
As d=52 is an upper bound for linear (104,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0174 seconds.