Drilling holes in the floor wont help at all. water will get in from underneath and make it worse.
Its a simple fix.
Above the back door on the outside is a black trim and one down each side of the rear door, pull the side ones off first, then prize off the top one.
The bracket under that top trim is held on with 4 big screws, remove the screws, fill the holes and around them with silicon sealer and put it back together.
The holes are sealed with a foam that rots away and somehow lets water get down into the storage box.