The generator matrix

 1  0  0  1  1  1  X  1  1  X  1  X  1  0  1  1  1  1  X  X  X  1  1  0  0  0  1  X  1  X  1  0  1  0  1  0  1  0  1  X  1  X  1  1  1  X  X  X  0  X  1  0
 0  1  0  0  1 X+1  1  X X+1  1  0  0  1  1  X  0  X X+1  1  1  X  X  1  1  1  X  0  1  0  1  X  1  X  1  X  1  X  1  0  1  0  1  1 X+1  1  X  X  0  X  X X+1  0
 0  0  1  1 X+1  0 X+1  1 X+1  X  X  1  X  1  1  1  X  X  X  1  1  0  0  0 X+1  1  0  1  X X+1  X X+1  0  1 X+1  X X+1  X X+1  0 X+1  0  1  1  1  X  0  0  0  X  0  1
 0  0  0  X  X  X  0  0  0  X  X  X  0  X  X  0  0  X  0  X  0  X  0  X  0  X  X  0  0  X  X  X  0  0  X  X  0  0  0  X  X  0  X  0  0  X  X  0  0  0  0  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+44x^50+44x^52+20x^54+16x^56+3x^64

The gray image is a linear code over GF(2) with n=104, k=7 and d=50.
This code was found by Heurico 1.16 in 0.0238 seconds.