I was able to print this case on a Makerbot Replicator 2, with probably the normal settings. I'll come back and change this Thing when I find out what the settings were. I made this nearly two years ago as of 1/7/19. Use Thingiview to see the back of the case. I didn't upload it upside down because it won't print upside down.
I have this uploaded to Thingiverse at https://www.tinkercad.com/things/0zz8m5ZXK8M.
Dat boi stencil
Sorry that I can't be super specific, but I also wasn't super scientific about my process. Basically, I found an image of dat boi on his unicycle, and opened the .gif in GIMP. GIMP shows every frame of a .gif as a layer, so I deleted the layers I didn't like as much as the one I chose. Having done that, I used a select-by-color tool to select the background of the image to get a stencil of him. Some of you will be thinking, there is no background, it's a gif! Yes, that's true, but I selected the transparency. Then I filled the transparent areas with a big black pencil (in GIMP of course) because only the transparent areas are selected, and it's really easy to cover all the areas with a pencil tool. The pencil tool is important because it is hard-edged and won't leave any transparency. Then invert the selection and color the inside white.
For the next step, you'll have to try a couple of different things unless you know a better way to make a raster graphic into a vector graphic. I found one of those anything-to-anything image converters online (might have been this one? https://image.online-convert.com/convert-to-svg) and exported my dat boi as a .png file. Upload dat boi and receive him in vector format. You may have to try a few times to convert your .png into a vector graphic. I might have just used one color/shape when I uploaded my .png (say, the positive white dat boi or the negative black dat boi). I don't remember clearly.
The next step is to take your .svg file to Tinkercad, give it some height, and use it to subtract (or add, I suppose) a shape to your existing design. Select Import, upload your .svg, and turn what probably came out as a "shape" into a "hole". This is done by selecting the shape/hole, after which a drop-down menu appears with "(O) Shape (///) Hole" in it. It looks somewhat like that. Select Hole to for a subtractive shape or shape for an additive shape. Move your extruded vector graphic (I'll call it a stencil) to your design. Once it's set in the proper place, join the stencil and your other object with the Group tool. Note that importing the stencil above into Tinkercad would create a Shape, but you could easily turn it into a hole as I did.
If your vector graphic comes out with a hole in it, you could either try to change what you uploaded to the .svg converter, or you could envelop that negative stencil you have in a similarly shaped rectangular prism, and subtract the negative stencil from the block. You'll now have your positive stencil as described above, and you should be able to make it into a Hole to subtract it from anything you like.
That probably comes off as craziness. Good luck.
tl;dr: remove your image's background; select by color; fill with single color. invert select; fill with another color. export. convert png>svg. upload svg to tinkercad. add/subtract until you have a usable stencil. profit.