So... is Code:Breaker finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: December 23, 2012
Manga finished: July 20, 2013
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Sakura Sakurakouji, a strong martial artist with a strong sense of justice, witnesses a disturbing scene: people consumed by blue flames. When she reports it, the evidence vanishes, leaving her questioning her sanity.
The next day, a mysterious transfer student named Rei Oogami appears, and Sakura recognizes him as the person responsible for the fiery deaths. Rei seems kind and popular, making Sakura's accusations seem unbelievable.
Sakura discovers Rei is a "Code:Breaker," a person who operates outside the law, dispensing his own brand of justice. Using unique powers, he punishes wrongdoers according to a strict code.
Disturbed by Rei's methods, Sakura resolves to guide him towards a more righteous path, hoping to prevent him from harming innocent people and redeem him from his vengeful ways. She stays close to him, trying to understand and influence his actions.