The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+130x^47+375x^48+740x^49+1220x^50+1510x^51+2151x^52+2624x^53+2827x^54+3142x^55+3107x^56+3344x^57+3152x^58+2566x^59+2039x^60+1480x^61+1063x^62+624x^63+377x^64+188x^65+55x^66+28x^67+14x^68+8x^69+2x^70+1x^90

The gray image is a linear code over GF(2) with n=224, k=15 and d=94.
This code was found by Heurico 1.16 in 33.3 seconds.