The generator matrix

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

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+140x^52+114x^54+149x^56+76x^58+27x^60+2x^62+2x^64+1x^100

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 0.0751 seconds.