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  X  1  0  1  1  X  1  1  1  0  X  1 X^2  X  0  1  1  X  1
 0  X  0  X  0  0  X X^2+X X^2 X^2  X X^2+X X^2+X X^2+X X^2 X^2  0  X X^2  X  X X^2  0  X X^2+X  X  0  0  0  X  0 X^2+X  0 X^2 X^2  0  X  X  0  X X^2  X X^2+X  X  0 X^2 X^2  0 X^2+X  0 X^2+X  X X^2  0  X X^2
 0  0  X  X  0 X^2+X  X X^2  0  X  X  0 X^2  X X^2 X^2+X  0 X^2+X X^2+X X^2 X^2 X^2+X  0 X^2+X  0  0  0 X^2  X  X  X  X  0  X X^2 X^2+X  X X^2+X X^2+X  0  0 X^2  0 X^2  X X^2+X  X X^2  0 X^2 X^2 X^2  0  X X^2+X  X
 0  0  0 X^2  0  0 X^2  0  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  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0 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+20x^50+62x^51+62x^52+118x^53+85x^54+156x^55+127x^56+92x^57+115x^58+40x^59+49x^60+6x^61+26x^62+22x^63+16x^64+8x^65+9x^66+6x^67+1x^68+2x^71+1x^94

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 0.153 seconds.