The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+42x^46+330x^47+925x^48+1386x^49+2163x^50+3184x^51+4233x^52+4624x^53+5872x^54+6104x^55+7161x^56+6608x^57+6243x^58+5034x^59+4188x^60+2778x^61+2005x^62+1258x^63+734x^64+338x^65+178x^66+90x^67+31x^68+10x^69+9x^70+7x^72

The gray image is a linear code over GF(2) with n=224, k=16 and d=92.
This code was found by Heurico 1.13 in 42.9 seconds.