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  1  1  1  1  1  1  X  1  1  1  1  1  1  X X^2  1  X  1  1  1  X
 0  X  0  0  0  X X^2+X  X  0 X^2  X X^2+X  0 X^2  X  X  0 X^2  X  X X^2+X X^2 X^2+X  0 X^2+X  X X^2  0 X^2 X^2+X  X  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2  X X^2  X  X X^2+X X^2
 0  0  X  0  X  X  X X^2  0 X^2 X^2+X X^2+X  X  X X^2 X^2  0 X^2+X  0  X  X  X  0  0 X^2+X X^2+X X^2+X X^2  0 X^2  0  X  X X^2+X X^2 X^2  0  0 X^2+X  0 X^2 X^2+X X^2+X X^2  0  X  X X^2+X X^2+X  X X^2+X X^2+X  X  X  0 X^2
 0  0  0  X  X X^2 X^2+X X^2+X  0 X^2+X X^2 X^2+X  X  0  X  0 X^2 X^2+X X^2+X  0 X^2+X X^2  0 X^2+X  0  X  X X^2 X^2+X X^2+X  0 X^2  0 X^2  0 X^2 X^2  0 X^2  X X^2+X  X  0 X^2+X  X X^2  X X^2+X  X X^2+X X^2+X X^2+X  X X^2+X X^2 X^2+X
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0  0  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+36x^50+50x^51+51x^52+90x^53+103x^54+122x^55+143x^56+118x^57+99x^58+78x^59+41x^60+46x^61+23x^62+6x^63+4x^64+2x^65+9x^66+1x^70+1x^102

The gray image is a linear code over GF(2) with n=224, k=10 and d=100.
This code was found by Heurico 1.16 in 0.15 seconds.