You have to use the highest level of error correction, to start with, and most generators default to the second (of four) levels, giving you no option to change it. At that highest level, it's best to keep the data as minimal as possible, to keep the code matrix coarse for reliable reading, but covering some of it is less unreliable than with the lower EC setting.
Most generators that allow the code to wrap around the logo are in the hands of the most predatory services, either unsecured or overcharging. It would be nice if someone would release a reliable, standalone generator (like ID's) that would allow logos.
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