Since we know from the existing entries in the X-Men franchise that Eric Lensherr (Magneto to be) helped Charles Xavier to build Cerebro, it would not be too much of a stretch to surmise that he had a hand in the construction of the plane as well (no doubt someone out there with a better working knowledge than me of X-Men lore can confirm if that is indeed the case).
There’s clearly quite a lot of green screen work going on here and the source site (CBM.com) speculates as to whether this island setting will be Muir Island for the film. If you click through to the site, you can scroll down and see what the various comments have to add as to which of the storyline strands from the X-Men universe might come into play here. For the moment, let’s just say that the plane looks cool, even in pieces.