You know that annoying yowling cats make while in heat? Well, "Heeeyyyy" is the verbal expression that girls (or guys) would use to broadcast their instinctual urges.
Much like saying "Hey" but not at all. This means you want to go all the way with the person you are saying it to. This only works through texting or similar applications.
Like other forms of the word "hey", this one is inherently sexual. "Heeyyy" implies that therecipient should tie themself to the bed and await the sender's arrival.