The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+38x^49+101x^50+126x^51+80x^52+242x^53+74x^54+386x^55+47x^56+370x^57+67x^58+202x^59+42x^60+110x^61+45x^62+46x^63+20x^64+8x^65+28x^66+8x^67+1x^68+5x^70+1x^92

The gray image is a linear code over GF(2) with n=224, k=11 and d=98.
This code was found by Heurico 1.16 in 0.335 seconds.