It's neither a bar code nor a QR code - it's kind of its own thing. After you buy your MK - on the Tickets page in the app, there'll be something like a card - top half is your name and MK level, bottom half is a wide pattern code.
I took a screenshot of that and emailed it to myself. Cropped it down to just the "card". I had some leftover photo paper, and printed it on that.
Nerd note: rather than resize the image to fit the card - I upped the screenshot resolution from 72 dpi to something like 400dpi to maintain the detail. Took a couple of test prints to get it to feel like the right size - I was trying to match the physical size that would be on my phone. (Though I'm not sure the exact size matters all that much.)
You probably won't want to go as far as I did - I'm enough of a perfectionist that I wanted it to look real-ish.
(Full details: I scanned the MK logo from the welcome package map. I printed the front and back separately on the same piece of paper, and cut them out oversize. Cut out a third blank piece of the same size from the remainder of the paper. I put spray adhesive on both sides of the third piece, and glued the front and back to it. Then cut it down to be the same size as an AP card. The third piece gave it enough thickness and hardness to almost feel like the real thing.)
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