The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+47x^52+102x^53+139x^54+24x^55+86x^56+48x^57+15x^58+25x^60+18x^61+4x^62+1x^64+1x^66+1x^86

The gray image is a linear code over GF(2) with n=220, k=9 and d=104.
This code was found by Heurico 1.16 in 0.0491 seconds.