The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+114x^53+54x^54+104x^55+30x^56+84x^57+30x^58+48x^59+20x^61+10x^62+8x^63+4x^65+2x^66+2x^69+1x^80

The gray image is a linear code over GF(2) with n=224, k=9 and d=106.
This code was found by Heurico 1.16 in 0.15 seconds.