The generator matrix

 1  0  0  1  1  1  X  1  1  1  0  1  X  X  1  1  0  1  1  0  1  1  0  0  1  1  X  X  1  1  X  1  1  0  1  1  X  0  1  1  1  0  1  X  1  1  0  1  X  X  0  0  1
 0  1  0  0  1 X+1  1  0  X  1  1 X+1  1  X  0  1  1  X X+1  1  X X+1  1  0  0 X+1  1  X  0  1  1  X  1  1  0  0  X  X  1 X+1  X  1  1  0  X  X  1 X+1  0  0  0  0  1
 0  0  1  1  1  0  1  X  1 X+1 X+1  X  X  1  0 X+1 X+1  0 X+1  1  1  0  0  1  1  X  X  1  X X+1  1  0 X+1  1  0  0  X  X  1 X+1 X+1  X  0  1  1 X+1 X+1  1  1  1  1  1  1
 0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  0  0  0  X  X  X  X  0  X  0  X  0  X  0  X  0  X  X  0  X  0  X  X  X  0  X  X  0  X  0  X  0
 0  0  0  0  X  X  0  X  0  0  X  X  0  0  X  X  0  0  0  X  X  0  X  X  X  0  X  X  0  0  X  X  X  0  X  0  X  0  X  0  0  0  X  0  X  X  X  X  X  X  0  X  0

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+30x^49+51x^50+44x^51+14x^52+18x^53+30x^54+10x^55+14x^56+10x^57+10x^58+2x^59+2x^60+6x^61+6x^63+1x^64+3x^66+2x^67+2x^70

The gray image is a linear code over GF(2) with n=106, k=8 and d=49.
This code was found by Heurico 1.16 in 0.032 seconds.