The generator matrix

 1  0  0  1  1  1 X^2  1 X^2 X^2  1  1 X^2+X  1  1  X  1 X^2  1  X  1 X^2 X^2+X  1 X^2  1 X^2  1 X^2  1  1  0  1  1 X^2+X X^2  X  1 X^2+X  1  1  1 X^2+X  1  X X^2  1 X^2+X  1  1  1  1  1 X^2  1  1
 0  1  0  0  1 X^2+1  1 X^2  1  1 X+1 X^2+X  0 X^2+X+1  X  1 X^2  X X+1  1 X^2+X+1 X^2+X  1 X^2+X  1 X^2+X+1  1  1 X^2+X  X  0  1 X^2+X+1 X+1  1  0  1 X^2+X  1  0 X^2 X^2+1  X X^2+X  1 X^2  1  1 X^2+X X^2+1 X^2+X X^2+X+1  1  1  1 X^2
 0  0  1  1  1  0  1 X^2+1  X X^2+X+1 X^2+1 X^2  1 X^2 X^2+1 X^2+X X^2+X  1  X X+1 X^2+X+1  1 X^2 X^2 X^2+1  0  X X^2+1  1 X^2+1  0 X^2+X+1 X^2+X  1 X^2+X  1  0 X+1  1 X+1  X X^2+X+1  1 X^2+1 X^2 X^2  0  X  X X^2 X+1  1 X^2+1 X^2+1  X X^2
 0  0  0  X  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  X X^2+X X^2+X X^2+X  X  X  X  X  X X^2+X  X X^2+X X^2  X X^2+X X^2+X X^2+X  X X^2 X^2+X X^2+X X^2+X  0 X^2  0 X^2+X  X X^2+X  X X^2  0  X  0 X^2  0  X  X
 0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  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+131x^50+224x^51+444x^52+368x^53+459x^54+404x^55+403x^56+280x^57+356x^58+252x^59+270x^60+160x^61+149x^62+76x^63+62x^64+24x^65+13x^66+4x^67+4x^68+10x^70+2x^74

The gray image is a linear code over GF(2) with n=224, k=12 and d=100.
This code was found by Heurico 1.16 in 0.674 seconds.