Hi- You can get a few floating shelves on the wall so they are approximately 5 feet high. Purchase some display brackets whose openings are wide enough to support the boxes. Place the boxes vertically on the shelves. Group the shelves together. Voila!

IMO show us your boxes . Your space too. I am not a lover of stuff displayed for no purpose so a bit more info for sure and pictures.

I don't see how you can both hang them on a wall and have them functional at the same time. You might consider placing them in a shadow box on a table, if your dog isn't too curious.

Oh sorry! I missed the keeping them functional part.

I have coffee tables with glass tops and a shelf below on which you can display the boxes.

So you can see them and the dog can't get a at them.

I have small stuff like this sitting on the bookcases in front of the books, and some of them are turned onto their side so you can see the tops. Most books you don't need to get to frequently, it's not a library, so I don't mind stacking stuff in front of them.

Wall-mounted cabinet with glass door front.