The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+36x^50+82x^51+142x^52+142x^53+119x^54+114x^55+80x^56+90x^57+62x^58+54x^59+31x^60+20x^61+33x^62+6x^63+1x^64+2x^65+1x^68+2x^69+4x^70+2x^78

The gray image is a linear code over GF(2) with n=220, k=10 and d=100.
This code was found by Heurico 1.16 in 0.125 seconds.