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

generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+20x^49+15x^50+20x^51+20x^52+11x^54+10x^56+12x^57+12x^59+5x^62+1x^64+1x^74

The gray image is a linear code over GF(2) with n=106, k=7 and d=49.
This code was found by Heurico 1.16 in 60.9 seconds.