The generator matrix

 1  0  1  1  1  0  1 X^2+X  1  1 X^2+X  1  1 X^2  1  1  1 X^2  X  1  X  1  1  1  X  1  X  1  1  0  1  X  1  0  1  1  1 X^2  1  0 X^2  1 X^2  1  1  X  1  1  X X^2+X  1  1  1  1  1  1
 0  1  1  0 X^2+X+1  1  X  1 X^2+X+1  X  1  1 X^2  1 X+1  0 X^2+X+1  1  1 X^2+X  1 X^2+1  X X^2+X+1  1  1  1  1 X^2+X+1  1 X^2+X+1  1 X^2  1 X^2+1  0 X^2+X  1 X+1 X^2  1  0 X^2  1  1  1 X^2+1  1  X  1 X^2+X+1  0  0 X^2+X X^2+X+1 X^2
 0  0  X  0 X^2+X  X  0  X  0  X X^2  0  X  0 X^2 X^2+X  X  X X^2+X X^2  0 X^2+X  X X^2  0 X^2 X^2+X  X X^2 X^2  0  X X^2  X  0 X^2  0 X^2 X^2  X  X X^2+X  X  0 X^2 X^2 X^2+X X^2+X  X X^2 X^2+X X^2  0  X X^2+X  0
 0  0  0  X  0  X  X  X X^2+X  0 X^2 X^2+X X^2  X X^2  X X^2+X X^2 X^2  0 X^2+X X^2+X X^2+X X^2+X X^2 X^2  0  X X^2+X X^2+X  0 X^2  X  X  X X^2 X^2  0  0 X^2+X  0  X  X  0 X^2 X^2  0  0 X^2+X  0  0  X X^2+X  X X^2+X  X
 0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  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+34x^50+158x^51+148x^52+284x^53+152x^54+226x^55+163x^56+258x^57+112x^58+176x^59+78x^60+116x^61+45x^62+42x^63+21x^64+10x^65+5x^66+6x^67+2x^68+4x^69+3x^70+3x^72+1x^74

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 0.258 seconds.