It is only available through an event that was over or through a trade with another game or person.
Here are the event Mew details so you know if you found a legit one.
You cannot find mew in Heartgold. You can only find it in emerald. You will have to trade it, out receive it in an event.
You can find a lot of Kanto Pokémon in HeartGold. You can find Mewtwo but not Mew. The only way to obtain Mew in HeartGold is to get in in a Trade, Action Replay, or in the Event that has passed.
I hope I helped you through this post.