The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  1  X  X  1  X  1 X^2  1  1  1  0  1 X^2 X^2  1 X^2+X  1  1  1  X  X  1  X X^2  0  1 X^2+X  0  1  1  1  1  1  0  1  0  1  X  1  1 X^2+X  1 X^2+X  1  1  X  1
 0  1  0  0  X X^2 X^2+X  1 X+1 X^2+1  1  X  1  1  1 X^2+X  1 X^2+X+1  0 X+1 X^2 X+1 X^2  1 X^2+X+1 X^2 X^2+X  X  0  1 X^2+X  1  0  1  1 X^2  X  1  0  0 X^2+X+1  1 X^2+1  X X^2+X+1  1  0  1 X^2 X^2+X+1  1 X^2+X  0  X X^2+X+1  1  X
 0  0  1  0  X X^2+1  1 X^2+1  0 X^2+1 X^2  1 X+1 X+1  X  0 X^2+X+1 X^2+X+1  1 X^2+X  1 X^2+X+1  X X^2+X  X  1  X  1 X^2+X+1 X^2+1  1 X^2+X X^2  0 X^2+X+1  0  1 X+1 X+1  0 X^2  X X^2+X  0 X+1 X^2+X+1 X^2+1 X^2+1 X^2+X X^2 X+1 X^2  1  1  0 X^2 X^2+X
 0  0  0  1 X+1  1  X X^2+1 X^2+X X^2+X+1 X^2+X+1 X+1  0 X^2+X X^2+1 X^2 X^2+X  1 X^2+X+1  0  X X^2  1 X^2+X+1  1 X+1  X  0 X+1  1 X^2+X X^2+1  1 X^2  0 X+1 X^2 X^2+1  1 X^2+1 X+1 X^2 X^2+X  1  X X+1 X^2 X^2  0 X^2+1  1 X^2+X X^2+X+1 X^2+1 X^2 X+1 X^2+X
 0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 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+116x^50+356x^51+523x^52+580x^53+789x^54+668x^55+836x^56+726x^57+778x^58+688x^59+676x^60+470x^61+386x^62+204x^63+169x^64+98x^65+54x^66+36x^67+17x^68+14x^69+5x^70+2x^72

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 2.38 seconds.