The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+120x^49+327x^50+502x^51+633x^52+690x^53+822x^54+868x^55+690x^56+714x^57+674x^58+534x^59+578x^60+442x^61+258x^62+160x^63+81x^64+48x^65+27x^66+16x^67+1x^68+4x^70+2x^73

The gray image is a linear code over GF(2) with n=224, k=13 and d=98.
This code was found by Heurico 1.16 in 2.32 seconds.