The generator matrix

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

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+172x^49+276x^50+624x^51+418x^52+868x^53+583x^54+912x^55+576x^56+984x^57+594x^58+838x^59+348x^60+476x^61+176x^62+170x^63+63x^64+52x^65+26x^66+10x^67+2x^68+8x^69+9x^70+6x^71

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 22.9 seconds.