The generator matrix

 1  0  0  1  1  1  0  0  1  1 X^2  1  1  0 X^2  X  X  1  1  1  1  1 X^2+X  1  X X^2+X  1  1 X^2 X^2+X  X  1  1 X^2+X X^2  1  1  1  0  1  1 X^2+X X^2+X  0  1  1  X X^2  1  1  1  1  1  1  1  1
 0  1  0  0  1  1  1  0 X^2 X^2+1  1  0  1  1  1  1 X^2  X X^2+1 X+1 X^2 X^2  1 X^2+1  1  X X^2+X X^2+X+1  1  1  1  X X^2  1 X^2+X  X X^2+X+1 X+1  1 X+1 X^2+X+1  1 X^2+X  1 X^2 X+1  X X^2+X X+1  1 X^2+X+1 X^2+X X^2 X^2+X  X  0
 0  0  1  1 X^2 X^2+1  1  1  0 X^2 X^2  1 X^2+1  1  0 X^2+1  1 X^2+X+1 X+1 X^2+X X^2+X X+1  0 X^2+X X^2+X+1  1 X^2+X X^2+X+1 X^2  0  X  0 X^2+X  1  1 X+1  0 X^2+X X+1  X  1 X^2+X  1 X^2+X X+1 X^2+1  1  1 X^2+1  X X^2+X+1 X^2+X X^2  0  1  X
 0  0  0  X  0  X  X X^2+X  X  X X^2+X X^2 X^2 X^2  X  0 X^2+X  0 X^2 X^2+X X^2 X^2+X X^2  0  X  0  X  X X^2  0 X^2+X X^2  X X^2+X X^2  X  X  0 X^2 X^2  0  0  X X^2+X  0  X X^2+X  0 X^2+X  X X^2 X^2 X^2 X^2+X  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+84x^51+186x^52+272x^53+312x^54+232x^55+192x^56+190x^57+133x^58+102x^59+108x^60+64x^61+43x^62+40x^63+19x^64+34x^65+23x^66+6x^67+6x^68+1x^70

The gray image is a linear code over GF(2) with n=224, k=11 and d=102.
This code was found by Heurico 1.11 in 0.11 seconds.