Mike Rhyner has taken to using this phrase in his introduction to the Hardline program.
The phrase apparently has a couple of meanings from military naval usages. It is more frequently expressed as "heave out and trice up."
In former days, it reportedly was a call to the crew to get out of bed (hammocks, whatever) and assemble on the deck to view floggings administered as discipline to crew members. All sailors were required to be present to view the punishment.
More recently, it is a call to the crew to get out of their bunks and fold the bunks up to the wall and secure them there.
If I get any other (better) explanations, I'll post.