The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+93x^48+150x^49+297x^50+410x^51+499x^52+740x^53+706x^54+762x^55+969x^56+824x^57+670x^58+714x^59+522x^60+292x^61+199x^62+138x^63+70x^64+34x^65+39x^66+20x^67+19x^68+8x^69+6x^70+4x^71+3x^72+2x^74+1x^78

The gray image is a linear code over GF(2) with n=224, k=13 and d=96.
This code was found by Heurico 1.16 in 3.6 seconds.