Don't scan as JPEG. Barcodes (QR codes are a subset of general "barcodes") are images that have very high contrast edges (typically a transition from pure white to pure black or pure black to pure white) and the fidelity of that edge is important to correctly decoding the code.
High contrast edges are the worst case for the JPEG compression algorithm, and the algorithm produces the most noise (compression artifacts) for high contrast edges (due to the nature of how the JPEG compression algorithm operates).
So combining JPEG compression with barcode images you have the worst two possible combinations, an algorithm that prefers nice sharp transitions (barcodes) and an algorithm that will create blurry edges (JPEG on high contrast edges).
Scan to PNG or old GIF or TIFF (using non-JPEG compression) but don't use JPEG for this particular purpose.