The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+60x^49+153x^50+226x^51+302x^52+340x^53+449x^54+414x^55+357x^56+418x^57+344x^58+320x^59+262x^60+196x^61+119x^62+52x^63+31x^64+8x^65+13x^66+6x^67+4x^68+7x^70+6x^71+3x^72+2x^73+2x^74+1x^78

The gray image is a linear code over GF(2) with n=224, k=12 and d=98.
This code was found by Heurico 1.16 in 32 seconds.