I caught mine with a Great Ball...
By the way here's my Rayquaza:
Level: 100
HP: 345
Attack: 359
Defense: 228
Special Attack: 332
Special Defense: 226
Speed: 212
Attacks:
Dragon Claw PP-24
Flamethrower PP-18
Thunderbolt PP-15
Surf PP-15
Pokemon League gets sweeped before they lay a finger on my Rayquaza (unless they use fakeout...). Remember stats can vary depending on nature. My Rayquaza is sassy. It takes a while to get it to level 100 but eventually you can get there.