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

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+46x^52+140x^53+70x^54+96x^55+33x^56+48x^57+18x^58+16x^59+8x^60+20x^61+13x^62+2x^66+1x^78

The gray image is a linear code over GF(2) with n=220, k=9 and d=104.
This code was found by Heurico 1.11 in 0.031 seconds.