The generator matrix

 1  0  0  1  1  1 X^2+X  X  1  1  1  X  X  1 X^2  0  1  X  1  1  1  1  1  1  X  X  1  1 X^2  1 X^2+X  X  1  1  1  1  0  0  0  1  1  1  1  1  1  X  1 X^2 X^2+X  X X^2  1  1  1  1
 0  1  0  0  1 X+1  1  0 X^2+X+1  X X^2+X+1  1  1 X^2  0  1  X  1  1 X^2  1 X+1 X^2+1 X^2  1  1 X^2  X X^2  X  1  X X+1 X^2+X+1 X+1 X^2+1  1  1  1 X^2 X^2+X X+1 X^2+1  X  X  1  1  1  1  1  1 X^2+X X^2+1 X^2+X+1  1
 0  0  1  1  1  0 X^2+1  1 X+1  X X^2+X X^2+X X+1 X+1  1 X^2  0 X^2+1  1 X^2+X+1  X X+1 X^2 X+1  0 X^2+X+1 X^2+X X^2+X  1 X^2  1  1 X^2+1  1 X+1 X^2 X^2+X  1 X^2  1 X^2+X  0  1 X+1 X^2+X+1 X+1 X^2+1 X+1 X^2+X X+1  0 X+1 X^2  X  0
 0  0  0  X X^2+X X^2 X^2+X X^2+X X^2+X  0  0  0 X^2+X X^2+X X^2+X  X  X X^2  0  0  X X^2  X  0  X X^2 X^2  X X^2  0  X X^2  0 X^2+X  X X^2+X X^2 X^2+X X^2 X^2 X^2+X  0  0 X^2+X  X X^2+X X^2 X^2 X^2+X X^2  X  0 X^2  0  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2  0 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+108x^49+276x^50+344x^51+497x^52+348x^53+459x^54+302x^55+418x^56+302x^57+323x^58+216x^59+213x^60+92x^61+78x^62+62x^63+23x^64+10x^65+15x^66+4x^67+4x^69+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 0.641 seconds.