Sharpening QR codes

My client gave me some high resolution images with QR codes on them. I need to downsize them to 1080x1920 so they display nicely on Full HD display.

Unfortunately, resampling the images makes the QR codes look a bit fuzzy, and makes any mobile phone QR code scanner software slow to recognize them.

I'm sure there is enough resolution for displaying sharp QR codes. The problem is that even the source images aren't that sharp and have resampling artifacts, so a simple nearest-neighbor resampling is still not good enough. Is there any image editing software that will recognize QR codes and can sharpen just the QR codes?

I could also just re-generate the QR codes, but my understanding is that QR codes can be generated in a number of ways: if you go to a few different free QR code generating websites and generate QR codes for the same URL, they can all look different, even though they will all work. I want to replicate exactly the kind of QR code that my client gave me, but I don't know how to determine exactly the generation parameters used by my client.

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