From the second edition (1989):
[App. a variant of bouge n.1]

A prominence from the back of the body of a carriage to carry parcels in; the ‘sword-case’. Felton.

1801 Felton Carriages I. 15 The sword-case, so called from its length and convenience for carrying swords or sticks, is sometimes called a boodge; the ends are made of thick boards.