One of my cats does the same. My assumption is he was taken from the mother cat too young so never learned how to do things properly.

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For the smell maybe try grain free food.

I have the same exact problem too, and if anyone has better explanations for it please tell me too, but, since my cat is 6 now, and this has been going on since she was a kitten, here’s what I’ve noticed:

First things first, cats often (but not always) shit outside of the box as protest.

For mine, it most probably had to do with how clean she thought the sand was.

Mine was always this way when I also had that closed box, as well as when I was using silicone sand when she was still small, but without the box.

It’s only recently, that I’ve gotten normal bentonite sand (clumping pee, easily fully removed), an open box (ventilation), and clean the sand almost always daily, that she has almost stopped. And when The Depression hits and I forget to clean it for 4 days or so, she does all the things mentioned, I’m assuming out of desperation, to make the bad smell go away.

Silicone sand needed to be fully replaced, and the box be thoroughly washed often, because it would at some point stop being able to contain the ammonia smell.

The closed box, I noticed, would both, contain and absorb bad smells itself, as well as incentivize me to not clean as often, since it didn’t bother me when it would start smelling a bit 😐, but the cat had to be in a shut box, faintly smelling the ammonia for many many seconds.

Full disclosure, bentonite sand has a few studies correlating it with cat respiratory problems, probably due to the dust that cheap bentonite has packed in. I’ve decided that it’s still probably for the best to buy bentonite with its dust filtered out(slightly more expensive), since it helps incredibly with cleanliness (if your cat has to groom unclean paws, that’s going to strain her kidneys and liver probably).

Also, the sand is both extra useless weight, and makes cleaning harder, because it clumps worse. The more expensive brand, where they remove the dust, makes everything easier, and probably much healthier.

In the exact same situation here, but a few months ahead. I was told by a vet that a farting kitten is an indication something is wrong with the diet. Our little girl does both, being really smelly on the box and walking around passing gas. The farting got less over time.

Problem is we also have two older cats so we can’t really get specialised food for one. We’d need special food for all three which can get really expensive.

We hope the problem will pass with time, maybe she needs to get used to the diet or something. Maybe at some point she’ll prefer doing her business outside and we’ll notice it less.

Fortiflora helped our cat. That and in time he learned how to cover his poops better. Sometimes kittens are derps

Her poops shouldn’t smell like roses, but the smell shouldn’t be so terrible that you can smell it from the next room either.
Are her poops solid? If they’re not, definitely talk to your vet, as she could be sick, and diarrhea is especially dangerous in kittens.
Assuming it’s not a medical issue, looking at the ingredients of that food, I think you might find the smell improves if you try a different food. One of my cats has a very sensitive stomach, and my vet said that ingredients such as fish, beef, lamb, corn (maize), soy, and wheat are frequent triggers for cats. I see that the first three ingredients of that food are on that list. For proteins, poultry (chicken, turkey, duck) or rabbit tend to be well accepted. I’ve had to switch my cats to 100% wet food, but my vet previously suggested Dr. Elsey’s chicken kibble, and they both liked it.