Hi newbie. In this case, set would be the word that you would use. Placed pretty much means the same thing and most of the time you can use either of them. When it comes to stories, though, the word "set" is used more often. You could use the word "placed" when you're talking about stories, but a better choice may be the phrase, "take(s) place." So your sentence would be: "I really enjoy stories that take place in the distant future." So, you're not wrong, really... the English language is just very picky. Does that answer your question?

placed = set = positioned (by author)