Peace and welcome to the forum,
Depends on your definition of 'remap' and how much power you want to extract from the engine. In theory, any modern engine can be remapped. But, for a non-aspirated 1.6 litre engine, is it worth it?
Without going down the turbo-charged and super-charged route (cost: hundreds, if not thousands of pounds), the most power you can add is an optimistic 10-15 bhp with 'cheap' mods (no pun intended) such as fully de-catted stainless exhaust system and air filters, etc.
You would be better off selling the car and buying a turbo-charged one for that matter...
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