update: Xcode 8.2.1 • Swift 3.0.2 or later
You need to convert it from milliseconds dividing it by 1000:
let epochTime = TimeInterval(1429162809359) / 1000
let date = Date(timeIntervalSince1970: epochTime) // "Apr 16, 2015, 2:40 AM"
print("Converted Time \(date)") // "Converted Time 2015-04-16 05:40:09 +0000\n"