The generator matrix

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

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+64x^49+118x^50+248x^51+344x^52+316x^53+396x^54+430x^55+408x^56+440x^57+376x^58+262x^59+229x^60+182x^61+118x^62+54x^63+36x^64+28x^65+11x^66+10x^67+5x^68+10x^69+4x^70+4x^71+1x^74+1x^80

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 0.748 seconds.