The generator matrix

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

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+119x^50+344x^51+469x^52+816x^53+569x^54+788x^55+703x^56+854x^57+607x^58+802x^59+551x^60+562x^61+353x^62+304x^63+160x^64+92x^65+42x^66+34x^67+4x^68+10x^69+6x^70+2x^73

The gray image is a linear code over GF(2) with n=228, k=13 and d=100.
This code was found by Heurico 1.11 in 0.891 seconds.