The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  X  1  1  1  1  0  1  X  1  1  1  0  1  1  0  X  1  1  0  1  1  1  1  0  1  0  1  X  1  0  1  X  X  1  1  0  X  1  1  X  1  1  X  1  1
 0  1  1  0  1  1  0  1  1  X X+1  1  1  0 X+1  0 X+1  1 X+1  1  X  0 X+1  1 X+1  0  1  1  0 X+1  1  0 X+1  1  0  1 X+1  1 X+1  1  1  1  1  1  1  X X+1  1  1  0  X  X  1  0  1  0  X
 0  0  X  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  X  X  X  X  0  0  0  X  0  0  0  X  X  0  X  X  X  X  0  X  0  0  X  0  0  X  X  X  0  X
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  0  X  0  X  0  0  0  X  X  0  X  X  0  0  X  0  X  X  0  X  X  X  0  X  0  X  0  X  0  X  0  0
 0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  X  0  X  X  X  0  X  X  X  0  X  0  X  X  0  X  X  X  0  X  0  X  0  0  0  0  0  0  X  0  X  0  0  0  0  X  X  X  X  X  X  X
 0  0  0  0  0  X  0  0  X  0  0  X  0  X  0  X  0  X  0  0  0  X  X  X  X  0  X  X  0  X  0  0  X  0  0  0  X  X  X  0  X  0  X  X  0  X  X  0  0  0  X  0  0  0  X  X  0
 0  0  0  0  0  0  X  0  X  X  0  0  X  X  X  0  0  0  X  0  X  X  X  X  0  0  0  X  0  X  X  X  0  0  0  0  X  0  X  X  0  0  X  0  0  X  X  X  X  0  X  0  X  X  0  0  0
 0  0  0  0  0  0  0  X  X  0  X  0  X  X  0  0  X  X  0  X  X  X  0  X  X  X  0  X  0  X  0  X  0  X  X  0  0  X  0  0  0  X  0  0  0  X  X  0  X  0  0  0  X  0  X  X  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+124x^50+116x^52+178x^54+110x^56+145x^58+112x^60+147x^62+31x^64+30x^66+8x^68+8x^70+2x^72+5x^74+4x^76+3x^78

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 29.1 seconds.