The generator matrix

1 0 0 0 0 1 1 1 0 X 1 1 0 1 1 X 1 0 1 1 1 0 X X X 1 0 1 1 0 1 1 0 1 0 X X 0 1 X 1 1 X 1 0 1 1 1 X 1 1 X 0 1 1 1 1
0 1 0 0 0 0 0 X 0 0 X X X 0 0 X 1 1 1 X+1 1 1 1 1 1 X+1 1 X X+1 1 X+1 1 X X 1 1 1 1 1 X X+1 X 1 1 X X+1 1 X+1 0 1 X+1 1 0 0 X X 0
0 0 1 0 0 0 1 1 1 X 0 X+1 1 X+1 X 1 X+1 X 1 0 X+1 X+1 X+1 1 0 X 0 0 X X+1 1 X 1 0 0 X+1 X+1 X 0 X X X 1 X 0 1 X+1 X 1 0 0 X X 1 X 1 X
0 0 0 1 0 1 X X+1 1 1 0 1 X 0 X+1 1 0 1 1 1 X X+1 X X+1 0 X 1 X+1 X+1 X+1 1 X X+1 X X 0 X X X 0 0 1 0 0 1 X+1 X+1 0 0 1 1 1 0 X+1 X X+1 0
0 0 0 0 1 X 0 0 X 1 X+1 X+1 1 X+1 1 X+1 1 0 1 0 X 1 0 X X+1 X+1 1 X 1 X+1 X X X X+1 0 X+1 1 X X 1 0 0 1 X+1 X+1 X X X 0 0 1 1 1 0 X+1 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+44x^50+84x^51+70x^52+94x^53+94x^54+80x^55+95x^56+64x^57+50x^58+52x^59+37x^60+54x^61+34x^62+28x^63+42x^64+32x^65+26x^66+8x^67+9x^68+10x^69+8x^70+4x^71+2x^72+2x^77

The gray image is a linear code over GF(2) with n=114, k=10 and d=50.
This code was found by Heurico 1.10 in 0.047 seconds.