I would suggest you decide what is "good" to your character.
I definitely do not agree your character is Chaotic, because of the strict adherence to a code (punish the wicked) you are clearly bent towards Lawful. Your character will not bend or sway because something feels "off" when carrying out your dogged pursuit of criminals.
As for the second axis, you can choose whether you begin as Lawful Good or Lawful Neutral, and see where you end up after playing. Lawful Good is an option because your character can have the ideology to try and be this way, without actually succeeding. Or perhaps too much lawbreaking will see your character surrounded by emotional turmoil. If you read up on the Paladin - Oath of Vengeance, your character's ideology fits nicely alongside this.
However, If you feel your character is willing to do this and not feel remorse for his actions, you are also capable of fitting into the Lawful Neutral category - following your code to the letter, as opposed to the spirit.
All in all don't let alignment dictate your character's actions, let your character's actions dictate your alignment.
I definitely do not agree your character is Chaotic, because of the strict adherence to a code (punish the wicked) you are clearly bent towards Lawful. Your character will not bend or sway because something feels "off" when carrying out your dogged pursuit of criminals.
As for the second axis, you can choose whether you begin as Lawful Good or Lawful Neutral, and see where you end up after playing. Lawful Good is an option because your character can have the ideology to try and be this way, without actually succeeding. Or perhaps too much lawbreaking will see your character surrounded by emotional turmoil. If you read up on the Paladin - Oath of Vengeance, your character's ideology fits nicely alongside this.
However, If you feel your character is willing to do this and not feel remorse for his actions, you are also capable of fitting into the Lawful Neutral category - following your code to the letter, as opposed to the spirit.
All in all don't let alignment dictate your character's actions, let your character's actions dictate your alignment.