The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X^2+X  1  1 X^3+X^2 X^2+X  1  1  1  0 X^3+X^2  1 X^2  X  X  1  1 X^3+X^2  0  1  1  1  1 X^3+X X^3  1  X X^3+X  1 X^3  X  1  1 X^3+X^2+X  1  1  1 X^3+X^2  1 X^2  1 X^3 X^2+X X^3+X^2+X  1 X^3+X  1
 0  1  0  0  0 X^3+1 X^3+1  1 X^3+X^2+X X^3+X X^3+X^2+X X+1 X^3+X^2+X+1  1  1 X^2+1  0 X^3  X X^2+X X^3+X^2+1  1 X^2+X  1 X^2+X+1 X^3+X^2+X+1  1  1 X^2 X+1 X^3+X X^3+X^2  1  0 X^2+X+1  1 X^3+X  1  1  1  X X^3+X  X X^2+X X^3+X+1  X X^3+X^2+X X^2  1  X  1  1 X^3+X^2 X^3+X^2+X  1 X^3
 0  0  1  0  1  1 X^2 X^2+1  0 X^3+1  1 X^2+1 X^2+X X^3+X^2+X+1 X^3 X^2  1  X  1  1  1  X  0 X^2+1 X^3+X^2+X  1 X^2+X X^2+X+1 X^3 X^3+X^2+1 X+1 X^3+X^2+X X^3+X^2+X+1 X^3+X X^3+X^2+1 X^3+X^2+1  1 X^3+X  0 X^2 X^2 X^3+X^2+1  1  0 X^3+X^2+X+1  1  1 X^2+1 X^2+X X^3 X^3+X  0 X^2+X X^3  1  X
 0  0  0  1  1 X^2 X^2+1  1 X^2+X+1 X^3+X X^2+1 X^2+1 X^2+X X^3+X^2+X X^2+1 X^2+X+1 X^3+X^2+X+1 X^3+1 X^3+X^2+X+1  0 X^3+1 X+1  1 X^2+X  0  X X^3+X^2  1 X^3+X+1  0 X^2 X^3+X X^3+X^2+X+1  1 X+1 X^3+X+1 X^3+X+1 X^3+1 X^3+X+1 X^3+X+1 X^3+1 X^3+X^2+1 X^3 X^3 X^2+X+1 X^3+X+1 X^3 X^3+X X^2  1 X^2+1 X^3+X^2  1  0 X^2  X
 0  0  0  0 X^3+X^2  0 X^3+X^2  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2  0  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2  0 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3  0 X^3 X^3 X^3+X^2

generates a code of length 56 over Z2[X]/(X^4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+229x^48+1274x^49+3647x^50+6778x^51+12843x^52+19588x^53+29525x^54+36548x^55+40462x^56+36630x^57+30838x^58+20088x^59+12681x^60+6258x^61+2853x^62+1150x^63+458x^64+160x^65+73x^66+26x^67+14x^68+10x^69+8x^70+2x^71

The gray image is a linear code over GF(2) with n=448, k=18 and d=192.
This code was found by Heurico 1.16 in 441 seconds.