You can't. It is not available on Pokemon Platinum.
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There is no such thing as the Shadow Luiga. To catch the Shiny Lugia though, you need to find the code.
shadow lugia is stronger black hole can beat almost ery pokemon.
I don't know anyone that has one {I wish I did}, but I know how to get one. Get the game Pokemon XD Gale of Darkness, catch Lugia, trade it on a GBA Pokemon game, and if you have Pokemon Pearl, Diamond, or Platinum, Migrate Lugia and 5 other Pokemon.
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ANSWER:no