The generator matrix

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

generates a code of length 57 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+35x^50+58x^51+86x^52+110x^53+99x^54+86x^55+95x^56+74x^57+43x^58+70x^59+39x^60+38x^61+35x^62+24x^63+16x^64+24x^65+30x^66+12x^67+15x^68+8x^69+14x^70+6x^71+4x^72+2x^73

The gray image is a linear code over GF(2) with n=114, k=10 and d=50.
This code was found by Heurico 1.16 in 0.135 seconds.