The generator matrix

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

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+39x^50+74x^51+72x^52+88x^53+113x^54+106x^55+81x^56+54x^57+50x^58+58x^59+44x^60+52x^61+28x^62+30x^63+35x^64+24x^65+19x^66+12x^67+16x^68+4x^69+7x^70+8x^71+7x^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 0.14 seconds.