The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  X  X X^2  X  X X^2  X  1  0  1  X  1  1  1  1  X X^2  1  1  0  1
 0  X  0  0  0  0  0  0 X^2 X^2  X X^2+X  X  0  0 X^2 X^2+X X^2+X  X  X  X  0  X  X X^2 X^2+X  X X^2+X X^2 X^2+X  X X^2 X^2  X  0  X  0 X^2  0 X^2  X  0 X^2+X  0 X^2  X X^2 X^2  0  0 X^2+X  X X^2 X^2+X  0  0
 0  0  X  0  0  0  0  0  0  0  0  0 X^2 X^2+X X^2+X X^2+X  X X^2+X X^2+X  X X^2 X^2+X  X X^2  X  X  X X^2  X  X  0  X X^2  0  X X^2 X^2  X X^2+X X^2+X  X  0  0 X^2 X^2  X X^2 X^2+X X^2 X^2+X X^2+X  0  0  0  X  0
 0  0  0  X  0  0 X^2 X^2+X  X  X  X  X X^2 X^2+X  X X^2 X^2  0 X^2 X^2 X^2 X^2  X X^2+X X^2  X X^2+X  X  X X^2+X X^2  X  X  0  X  0  X  0  X  0 X^2+X X^2+X X^2 X^2 X^2 X^2 X^2+X X^2 X^2+X X^2+X X^2 X^2+X X^2+X  X  0  0
 0  0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  X  X  0 X^2  X  0 X^2+X X^2+X X^2+X  X  0 X^2+X X^2+X X^2  0  0 X^2  X X^2 X^2+X  0 X^2 X^2+X X^2  X  0  0 X^2+X X^2  X  X X^2 X^2 X^2+X  0  0  0  0  X X^2+X  X X^2  0
 0  0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2  X  X  0  X  0 X^2+X X^2+X  0  X X^2 X^2+X  X  X X^2  0  0 X^2  X X^2 X^2+X  0 X^2  X  0  0 X^2  X  X X^2  X X^2+X  0 X^2  0  0  0  0 X^2+X X^2  X X^2+X X^2  0  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+36x^46+100x^47+184x^48+202x^49+258x^50+356x^51+462x^52+534x^53+705x^54+880x^55+852x^56+840x^57+720x^58+578x^59+408x^60+308x^61+240x^62+170x^63+115x^64+86x^65+78x^66+26x^67+26x^68+14x^69+10x^70+2x^71+1x^86

The gray image is a linear code over GF(2) with n=224, k=13 and d=92.
This code was found by Heurico 1.16 in 4.53 seconds.