The generator matrix

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

generates a code of length 57 over Z2[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+74x^49+100x^50+146x^51+173x^52+132x^53+168x^54+120x^55+123x^56+122x^57+105x^58+134x^59+103x^60+102x^61+106x^62+74x^63+60x^64+68x^65+46x^66+32x^67+20x^68+14x^69+18x^70+6x^71+1x^74

The gray image is a linear code over GF(2) with n=114, k=11 and d=49.
This code was found by Heurico 1.16 in 0.483 seconds.