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  X  X  X  X  0  X  0  0  X  0  X  X  X  X
 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  X  X  X  X  0  0  0  0  0  X  X  X  X  0  X  X  0  X  0  X  X  0  X  X
 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  0  0  0  0  0  0  0  0  X  X  0  0  0  X  X  X  X  0  X  0  X  X  X  0
 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  0  X  X  X  0  X  0  0  X  0  0  X  0  0  0  X  0  X  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  X  0  0  X  X  0  0  0  X  X  0  0  0  X  X  0  0  X  0  X  X  X

generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+36x^50+7x^52+2x^54+7x^56+8x^58+2x^62+1x^76

The gray image is a linear code over GF(2) with n=104, k=6 and d=50.
This code was found by Heurico 1.16 in 53.3 seconds.