I didn't know much about Code: Breakers than what the description tells us, which is also very misleading. Sakura, the main girl, is definitely not good in martial arts, however she's not a person to mess with either.
Sakura is just a simple high-school girl, until she sees Ogami exterminating a bunch of people with blue fire. Later on we find out that he is a Code: Breaker (number 6), and works for an organization that makes him kill 'evil' people. Code: breakers are people with a special ability, Ogami's ability is a blue flame which burns everything to well .. nothing, but he likes to say 'burn to ashes'. Sakura doesn't want him to kill people, she believes that there are other ways to change evil people's minds (and she preaches this A LOT throughout the entire manga). Ogami was about to kill Sakura but finds out that he can't, Sakura is a 'rare-kind', one who can dispel any ability from any code: breaker.
The story had a nice set-up within the first few chapters, but it moves on from that story plot and introduces a lot more code: breakers, adds in a bunch of comedy, and it generally tries to figure out what KIND of story it wants to be. So the beginning is very serious, then it's pretty funny without much plot, and then it finally gains some ground and we get something that resembles a plot.
Code: Breaker is funny and while it seems to lose its way throughout the middle, the characters are interesting and funny. Some might say Sakura is annoying, but I find her much of an improvement compared to the ditzy and air-headed heroines that plague all kinds of manga. Sakura isn't ditzy, she knows what's going on, and she sticks with her ideals. Slowly, she changes Ogami's views - and there might even be a possibility of romance between them. She's not always the damsel in distress, she seems to handle herself just fine when she's pushed to use her rare-kind's ability. In fact, she saved 4 code: breakers all on her own!
Ogami is very much like Light from Death Note, because he really just kills people on a whim (much to Sakura's dismay). Although he does show signs of extreme embarrassment in later chapters, unlike the always cool and collected Light. With Sakura nagging him and hanging around him all day long, he slowly changes a bit. He doesn't realize it, but he's grown very much attached to Sakura and wants to protect her. Because of this, he wants to become stronger, so that he won't just watch and see Sakura get hurt by the person he hates most. Despite Sakura's nagging not to kill, he still goes and kills people on a whim - if he can that is.
All the other code: breakers are funny and interesting too. Despite the fact that they're supposed to be all emo and stuff because they kill people, they seem like regular young teenagers that are having fun with each other most of the time. Of course, that changes in the later parts of the manga because it's finally continuing its plot.
Anyways, Code: Breaker is funny and interesting, and while it doesn't seem to have much of a direction in the beginning, it'll get better. Just keep reading!