As I'm thinking about it, he doesn't really follow an external code at all, just his own simple sense of right and wrong. This generally involves protecting the helpless and innocent from those who would prey on them. He tends to categorize people as either villains, victims, or neither, based on their behavior. He is not above roughing someone up whom he categorizes as a villain in order to get information, and he has no compunctions about killing a serious villain outright if only to prevent that person from victimizing others in the future. He takes no particular joy in this. To him, it's just an unsavory but necessary part of his job. He evaluates each person on his or her own merits, and he doesn't waste his time on petty wrongdoers, focusing instead on serious villains.
I'd go with very much Chaotic Good.
I've evolved to a slightly non-standard view of the Law/Chaos axis because of a few issues if you say "lawful characters follow the rules" and/or "chaotic characters follow no code". That would mean that the Paladin is expected to abide by laws that clearly lead to suffering (say, slavery as per pre-war South), which is absurd. Nor could you ever have a CG character who could actually
explain his position, which is equally absurd.
Instead, I tend to view Lawful as an indication that the character tends to think of the
group while Chaotic means he thinks in terms of individuals. What I mean by this is that a Lawful character will look at clans, races, nations, even clubs or guilds as whole entities. This could be the proletariat vs. the 1%, the enslavement of an "other", or the weight a good king feels from his title. A Chaotic character, on the other hand, tends to look at each situation and the parties individually. It's not just "a rich person", but could be someone who either takes personal responsibility with his money or is just plain greedy. Not every murder warrants the death penalty, but that guy with rage in his eyes just might be a mad dog. Ethically Neutral (Gygax referred to the Law/Chaos axis as ethics) characters balance the two in some way, whatever that looks like -- if they don't have a strong opinion or instinct about it, that's probably Neutral.
The tendency to group people/things may come from a desire for order or order may be a natural outgrowth of a tendency to group things. Likewise, seeing individuals instead of groups may birth a disregard for rules or it could be the other way around. Sometimes, the Lawful character just thinks everyone should do what he says or the Chaotic character just wants to be left alone.
The Good/Evil (moral) axis refers to whether a person looks for what benefits others or themselves first, and by how much. An extremely Evil character would even be willing to kill/maim another just for the entertainment value or because it was easier than asking them to move out of the way. An extremely Good character is likely to court martyrdom. Morally neutral characters are generally capable of justifying small, non-personal harm to others for their own gain -- stealing some bread because they're hungry or even making a career of petty theft. They might also lie (but not about anything important) or be willing to turn a friend over to the wicked queen ("it was him or me").
A category of "evil-hating neutrals" has always been a mainstay of D&D adventuring parties, though. That means they're generally in it for the money (or revenge, etc.), but they recognize that they do have people they care about or just that Iuz taking over the Flaness would be horribly inconvenient. Depending on where the vengeance vs. justice pendulum swings, a character like you originally described could be N or CN. The fuller description almost screams CG, to me, though.