The generator matrix

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

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+78x^46+224x^47+436x^48+690x^49+1122x^50+1578x^51+2021x^52+2574x^53+2838x^54+2968x^55+3327x^56+3320x^57+3025x^58+2788x^59+1999x^60+1362x^61+1023x^62+588x^63+318x^64+228x^65+153x^66+42x^67+24x^68+16x^69+17x^70+4x^71+2x^72+2x^73

The gray image is a linear code over GF(2) with n=224, k=15 and d=92.
This code was found by Heurico 1.16 in 36.9 seconds.