Rank 3 investigators can't have Quinque, mate. Curious, but how much of Tokyo Ghoul have you watched/read? Personally, I'm kinda behind. I'm about 3/4 through the original manga, I keep with the anime, and I receive frequent spoilers on Tokyo Ghoul:re, so I'm somewhat informed, but I'm wondering how much would be a spoiler to you.

Also, you don't need to worry about Quinque, mate. As long as you change your character's rank, your Quinque can be almost anything. Just wait until you see what I got away with ;D

EDIT: Oh, I think I see the problem. You got things backwards, m80. You start off Rank 2 if you've graduated traditionally from the CCG Academy, and Rank 3 if you become an investigator through unorthodox circumstances like Juzou. Promotion for your guy would be becoming a 1st rank investigator, not the other way around.