The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+623x^50+1373x^52+1534x^54+1477x^56+1294x^58+1109x^60+550x^62+162x^64+55x^66+6x^68+8x^70

The gray image is a linear code over GF(2) with n=224, k=13 and d=100.
This code was found by Heurico 1.11 in 748 seconds.