The only code that Dom Toretto lives and swears by is family! He might be a thug and criminal by definition but his actions have always been motivated by his drive to care for his family.
He feels this innate responsibility for the people he cares for. This extends not only to his actual family like Mia but also to his friends.
As does he say in Furious 7,
"I don't have friends. I got family."
Dominic and his crew regularly take the law in their hands. Agreed that their motives are not always altruistic at best but most often than not they are pushed into a corner and conflict is their only way out.
Dom makes his views abundantly clear to Owen Shaw in Fast & Furious 6 -
"Your brother never told you never to threaten a man's family? It's a pretty stupid thing to do."
A person's code is the philosophy they believe in, something that defines who they are. These are a set of rules that ought to be unwavering, even in moments of extreme pain or difficulty. Dom's belief in his code is so strong that he never forsakes them.
Again in Fast & Furious 6, after he's been shot by Letty, he says to Brian -
"You don't turn your back on family. Even when they do."
Above all, his love for his family trumps everything. To Dom, family is the only thing worth living for. And if the situation demands it, then dying or it too! Caring for his family, providing for them and doing right by them is the code Dominic Torreto lives by.
At the end his philosophy is simple, something that he vocalizes in Fast 5 while talking to his crew -
"Money will come and go. We know that. But the most important thing in life will always be the people in this room, right here, right now. Salut mi familia."