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the download keeps failing, and it says I need a code to connect gog galaxy to gog, how do I get such a code?
https://www.gog.com/galaxy?utm_source=webtekno

You download Galaxy, log in to Galaxy and download Gwent. It needs Galaxy because it uses the online features of it being it is an MMO game.
You forgot to say that you need to download the fully optional client!