The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+92x^51+213x^52+210x^53+334x^54+214x^55+226x^56+172x^57+153x^58+82x^59+111x^60+48x^61+66x^62+38x^63+32x^64+32x^65+13x^66+6x^67+2x^69+2x^70+1x^72

The gray image is a linear code over GF(2) with n=224, k=11 and d=102.
This code was found by Heurico 1.16 in 0.203 seconds.