The generator matrix

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

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+107x^48+332x^49+756x^50+896x^51+1115x^52+1214x^53+1470x^54+1460x^55+1784x^56+1402x^57+1613x^58+1212x^59+1111x^60+762x^61+502x^62+302x^63+186x^64+82x^65+31x^66+16x^67+16x^68+10x^70+2x^71+2x^74

The gray image is a linear code over GF(2) with n=224, k=14 and d=96.
This code was found by Heurico 1.13 in 3.16 seconds.