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You're not including spaces (0x32). Even then, this won't create all possible tweets since it is limited to a little tiny bit of the whole unicode space. Please don't think that I don't like your idea, but it might benefit from some improvments :)
Thanks! I've added a unicode charset, but it's pretty sparse.
Interesting experiment. Reminds me of Borges's "The Library of Babel".

Would be interesting to see all tweets using only lower-case alphabet plus spaces. (~ 2.5e200)

This could actually be useful if the tweets were assigned indexes. You could create a tidy little cipher.
This is impressive from the simple fact I can type any tweet-able sentence and it is there. Now, this is kinda obvious because it is what the post is about.

But, doing it. Actually typing in a sentence. Every sentence. Even what I am writing now is there. Really, take one, copy and paste, like this one, and it is there.

The first thing I thought of when seeing this was the short story "the nine billion names of God." Except that this is a hair more than nine billion... Seriously though, this is impressive; it's so quick!
It's really, really fast. Congrats ! No accents though: try searching for `é` for example.