The generator matrix

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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+164x^51+202x^52+420x^53+296x^54+528x^55+360x^56+536x^57+239x^58+394x^59+220x^60+236x^61+115x^62+174x^63+63x^64+80x^65+21x^66+18x^67+18x^68+8x^69+1x^70+2x^71

The gray image is a linear code over GF(2) with n=228, k=12 and d=102.
This code was found by Heurico 1.16 in 0.732 seconds.