The generator matrix

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

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+56x^52+4x^56+3x^64

The gray image is a linear code over GF(2) with n=104, k=6 and d=52.
As d=52 is an upper bound for linear (104,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 6.67 seconds.