The generator matrix

 1  0  0  1  1  1  0  1  1 X^2  X  1  0  1  1  X  1 X^2+X  X  1  1 X^2+X  1  1  1  X X^2+X  1  X X^2  1 X^2+X  1  1  1 X^2  1  1 X^2  1 X^2+X  1  1 X^2  1  1  0  1  1 X^2 X^2 X^2+X  1 X^2+X  0  1  1
 0  1  0  0  1  1  1 X^2  0  X X^2+X  1  1 X^2+X+1 X+1  1  X  1  1 X^2+X X+1  1  1 X^2+1  0  1 X^2  X  1  1 X^2+X+1 X^2  0 X^2+1 X^2+1  X  X X^2+X X^2 X+1  1 X+1  0  1 X^2+1  1  1 X^2+X+1 X^2  X  1 X^2 X+1  1  1 X+1  X
 0  0  1 X+1 X^2+X+1  0 X+1  X X^2+1  1  1  1 X^2+1  X  0 X^2 X^2+X X^2+1 X^2+X+1 X+1 X+1  X  1 X^2+X X^2+X  X  1 X^2+1  1  X X^2+1  1 X+1 X^2+X+1  0  1 X^2  X  1 X+1 X^2 X+1  1  0  0  1  0  1 X^2  1  1  1  0 X^2+X+1  X X^2+X+1 X+1
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0
 0  0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+224x^50+172x^51+750x^52+244x^53+1067x^54+384x^55+1082x^56+488x^57+1149x^58+352x^59+987x^60+248x^61+539x^62+112x^63+214x^64+40x^65+75x^66+4x^67+35x^68+4x^69+14x^70+3x^72+4x^74

The gray image is a linear code over GF(2) with n=228, k=13 and d=100.
This code was found by Heurico 1.16 in 2.99 seconds.