I'd tell you to look at indigenous pre industrial economies, but you'd probably say they aren't still around (and again, not self identified as communist).
I'd tell you to look at Mondragon, but that's a large democratic worker co-op making billions of dollars, not a communist country. That's fair.
So let's talk about Portugal post carnation revolution. Portuguese politics is dominated by the socialist party, the social Democratic party, the communist party, and the green party. The State owns many major businesses and many more companies through trust in the public interest. You might say they aren't a communist country, I might say they aren't a Stalinist communist country. But they self identify as socialist country.
I'd encourage you to read up on Ujamaa and the Arusha Declaration, prime minister Julius Nyerere's plan to lift Tanzania out of poverty in the 70s. It unfortunately failed due to world events. But seriously, consider reading up on it. It wasn't perfect, maybe it would have gone autocratic. More broadly I could spend days writing comments about African Socialism.
You can look at the Spanish revolution and the communists who fought against the Stalinists and the Soviet Union. Eventually they were militarily crushed, but they were worker led, libertarian socialist economies with millions of people, eventually stomped out by Stalinists.
I don't think I met the bar of your question, but I hope that I dispelled the idea that there is only one kind of communism.
I also hope I provided at least some interesting things to go dive into on Wikipedia. At the very least I hope I'm providing some novel intellectual stimulation.
There is a hugely rich variety of models, and not all of them require a unitary authority or harsh anti democratic laws. There's a very interesting historical and modern discussion around many, many other models, and not engaging with it (or saying that all these models are the same as the Soviet model) is ignoring a lot of well thought out theory and practice.