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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+19x^50+30x^51+49x^52+8x^53+72x^54+72x^55+254x^56+48x^57+254x^58+60x^59+55x^60+8x^61+27x^62+24x^63+20x^64+10x^66+6x^67+4x^68+1x^70+1x^72+1x^106

The gray image is a linear code over GF(2) with n=228, k=10 and d=100.
This code was found by Heurico 1.16 in 0.167 seconds.