The generator matrix

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

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+108x^51+182x^52+344x^53+158x^54+274x^55+169x^56+212x^57+96x^58+184x^59+71x^60+62x^61+62x^62+66x^63+22x^64+16x^65+4x^66+8x^67+3x^68+6x^69

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 0.208 seconds.