The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+82x^49+253x^50+402x^51+435x^52+442x^53+428x^54+382x^55+352x^56+320x^57+283x^58+204x^59+176x^60+138x^61+75x^62+54x^63+27x^64+10x^65+16x^66+14x^67+1x^68+1x^70

The gray image is a linear code over GF(2) with n=220, k=12 and d=98.
This code was found by Heurico 1.16 in 0.539 seconds.