Making a litterbox from a plastic bin - sizing and door placement?

We've been having trouble with Oreo spraying the back of the covered litter boxes and the urine running out onto the floor.

We've tried a large bin with the lid off, but then Mr Underfoot rolls in the litter. I can't imagine that it's good for him to lick that litter dust off his fur. I've never seen him roll in the covered boxes, so I'd like to try making a litter box from a large Rubbermaid-type bin and keeping the lid on, and cutting a hole in the top or in the side for the cats to get in.

I need the box to be tall enough for our biggest cat Oreo, so that he'll be willing to use a box with a lid on it. He stands about 14 to 15" high at the base of his tail (he wouldn't hold still to be measured, and he's probably a bit higher than that when he sprays because he stands up tall when he's spraying).

How tall should the bin be, for him to be comfortable? And should I cut the hole in the top, or in the side, and how large should the opening be?

Thanks

The dimensions of my box are: 15 1/2" tall x 14" wide x 18" long ( we will be upgrading to a larger taller box soon) its a 18 gallon sterilite tub with a 9 inch hole on one end of the lid-- i just put one of my large boilers on the box and tracedaround it in permanant marker and used wire cutters to cut the plastic lid. I also drilled a bunch of little holes in the other end of the lid to allow litter to fall back into the tub when he jumps out on the box top.

here are two pictures of my rubbermaid litter box for Peanut Butter 6 mo old kitten-- Hes a litter thrower so this is what solved the problem for the most part...

litterbox side
litter box top

i would probably suggest at least a 20" tall box Thats about the size we will be doing in the next couple of weeks. good luck!

Thank you!