There are no heroes in this dark world of isolation and alienation. Gogol does seem to suggest that the only recourse to the denizens of this existence is to find a distraction to make the mind soar above the dirt and the grime, even if only for a time.
Indeed, the narrator's own flights and digressions provide an example: we can't help but laugh at the black humor that the narrator shows with such relish and detail. In dark times, satire and lampooning -- keeping a sense of humor -- is heroic.
Yet, even while Akaky revels in the though of his new overcoat and becomes more than a zombie for a day, the narrator reminds us what kind of world he lives in. It's one that does its best to pummel delight, as Akaky soon learns from thugs and those he solicits for help.
At the end, however, the Person of Consequence does have a -- perhaps fleeting -- thought that he should think before he is ever harsh to another the way he was to AA. Maybe this is all the heroism that can be mustered.
There are no heroes in this story.
Gogol creates a dark, naturalistic world where man is at the mercy of forces beyond his control - government, social class, and baser elements of his own nature. In this environment, I think it can be argued that a hero is one who recognizes humanity and need in others and possesses the courage to do something about it. There are three instances where characters do indeed recognize the situation, but all are ineffectual in alleviating it. The new employee who "shudder(ed) when he perceived how much inhumanity there was in man" does nothing more than moan, Akaky's fellow workers who take a collection for him raise "only a trifling sum", their money spent on more "important" things, and the Very Important Person feels remorse at his treatment of Akaky, but is quickly distracted by self-indulgent pursuits.