From YPPedia
Booched duty puzzle.

Originating from the Booched rating (lowest) for puzzles, this term is now used universally as a replacement for making a mistake or messing something up. The phrase "chat booch" refers to sending a message over the wrong chat channel and inadvertently broadcasting that message to an unintended group. A "Booched Pillage" is a pillage which has not worked out well. A ship which is on a booched pillage will commonly have full or almost full damage and bilge, and may not have any rum or cannon balls.

The word is a reference to Grady Booch.

The word is also a more piratey-sounding variant of the term 'botch', which means 'to ruin through clumsiness'.