How can I get a floating body in texinfo?  

You don't.  Sorry.  Texinfo has needed an @figure command for a long time.

    Something like the LaTeX
    figure environment, so I can put example code in boxes to one side.

If you like boxes (ugggggh, IMHO :) around stuff, Texinfo offers @cartouche.
It's not great, but it's what there is.

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