The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  1  0  0  1  1 X^2+X  1  1  1  X  1  X  1 X^2+X  1 X^2 X^2+X  1  1  0  1  1  0  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2 X^2+X  1  X  1
 0  1  1  0 X^2+X+1  1 X+1 X^2+X  1 X^2  1 X^2+1  X X+1  1  1  0 X^2+1  1  X X+1  X  1  1  1 X^2+X+1  1 X^2+X  1  1 X^2+X X^2+X+1  1 X+1 X+1  1 X+1  1 X^2 X^2+1  1 X^2+X X+1 X^2 X^2+X X^2 X^2+X X^2+X+1 X+1  X X^2  1  1  1 X^2+X  0 X^2+X
 0  0  X  0 X^2+X  0 X^2 X^2  X X^2+X X^2+X X^2  X  X  X  0  X X^2 X^2+X X^2 X^2 X^2+X X^2 X^2+X  X X^2 X^2 X^2 X^2+X  X  0  X  0  0  X X^2 X^2 X^2+X  0 X^2+X  X  X X^2+X X^2+X X^2  0  0  0  0  0 X^2+X X^2 X^2  X X^2 X^2+X  X
 0  0  0  X  0  0  0 X^2 X^2 X^2 X^2  0  0  X  X  X X^2+X  X  X X^2+X  X X^2+X X^2+X X^2+X  X X^2+X X^2  0  0  0 X^2+X X^2 X^2  0 X^2+X X^2+X X^2+X  X  X X^2+X  X X^2+X X^2  X  X  X  X X^2  0  0 X^2 X^2  X X^2  X X^2  X
 0  0  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0  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+61x^50+172x^51+224x^52+322x^53+365x^54+388x^55+401x^56+328x^57+381x^58+390x^59+344x^60+304x^61+187x^62+78x^63+39x^64+32x^65+25x^66+22x^67+12x^68+6x^69+3x^70+6x^71+3x^72+1x^74+1x^78

The gray image is a linear code over GF(2) with n=228, k=12 and d=100.
This code was found by Heurico 1.16 in 0.794 seconds.