The generator matrix

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

generates a code of length 56 over Z2[X]/(X^4) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+328x^49+1704x^50+3742x^51+6906x^52+10758x^53+14460x^54+17522x^55+19276x^56+18830x^57+15030x^58+10612x^59+6358x^60+3126x^61+1596x^62+562x^63+159x^64+36x^65+38x^66+10x^67+4x^68+8x^69+4x^70+2x^73

The gray image is a linear code over GF(2) with n=448, k=17 and d=196.
This code was found by Heurico 1.16 in 112 seconds.