Had you read the report carefully, you can see that Wilbo is only warning them based on the fact that you didn't provide any full screenshots. In your case, my only assumption with a punishment that "severe" for simple spamming is that you had spammed a few times prior to the 24 hour tempban.
You can still use Gyazo, theres nothing restricting you from using it. Instead of just getting the text, get the whole minecraft window, or the whole screen. If anything, grabbing the whole screen is faster than trying to grab a couple lines of text. Or so it's been easier in my experience.
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