The generator matrix

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

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+78x^47+496x^48+754x^49+1163x^50+1894x^51+2011x^52+2380x^53+2771x^54+3150x^55+3272x^56+3142x^57+3099x^58+2454x^59+2102x^60+1610x^61+1023x^62+656x^63+327x^64+192x^65+102x^66+52x^67+15x^68+18x^69+2x^70+4x^71

The gray image is a linear code over GF(2) with n=224, k=15 and d=94.
This code was found by Heurico 1.13 in 11.2 seconds.