The generator matrix

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

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+72x^51+274x^52+442x^53+450x^54+420x^55+312x^56+462x^57+327x^58+350x^59+242x^60+234x^61+156x^62+124x^63+95x^64+42x^65+51x^66+24x^67+12x^68+4x^69+2x^75

The gray image is a linear code over GF(2) with n=228, k=12 and d=102.
This code was found by Heurico 1.11 in 0.234 seconds.