This 2008D penny has a very light coat of copper that has rubbed off on the some raised areas. Looks like the real thing?
Too heavy. A standard copper plated zinc cent weighs 2.5 grams +/- .1 grams so 2.4 is within specs for a normal coin, or one that has have the copper removed, or even a normal one one that has been lightly plated with zinc after it left the mint. An aluminum cent would weigh approximately .93 grams. So your coin is almost 2.5 times heavier than it should be to be aluminum.
sound like what you have is a normal zinc coin with some of the copper plating worn off or removed in some way. after 1982 our US cents are a zinc core with a thin copper plating. the zinc does look like aluminum when it is exposed and polished.