The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+86x^50+312x^51+326x^52+492x^53+375x^54+474x^55+363x^56+340x^57+272x^58+318x^59+182x^60+228x^61+103x^62+102x^63+62x^64+28x^65+12x^66+10x^67+10x^68

The gray image is a linear code over GF(2) with n=224, k=12 and d=100.
This code was found by Heurico 1.11 in 0.234 seconds.