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

generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+53x^48+32x^50+89x^52+32x^54+42x^56+6x^60+1x^100

The gray image is a linear code over GF(2) with n=104, k=8 and d=48.
This code was found by Heurico 1.16 in 0.0308 seconds.