8 groups of 3, people from each group go vs each other, winners of each group go to the quarterfinals? That's how I'd do it
That would take 6 weeks for groups, 2 weeks for quarterfinals, 2 weeks for semifinals, 1 week for final, 11 weeks... maybe a little too much? The alternative with seeded competitors (8 seeded ones go into 1/8th finals, 16 others have a play-off) would take 9 weeks.