The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+66x^50+84x^51+279x^52+90x^53+327x^54+108x^55+274x^56+88x^57+275x^58+60x^59+184x^60+42x^61+85x^62+30x^63+29x^64+4x^65+10x^66+4x^67+1x^68+3x^70+2x^71+1x^74+1x^78

The gray image is a linear code over GF(2) with n=224, k=11 and d=100.
This code was found by Heurico 1.16 in 0.263 seconds.