I want to make a game similar to Tiny Miner without having to write any code but I'm not sure which game engine to use. What are your suggestions?

No code at all is technically impossible, regardless of the engine you choose. Even visual programming (like Unreal Engine Blueprints) is still code, just that you code using connected blocks instead of text.

That said, if you don't have any experience with programming (of any kind), this game might be a bit too much for you to start. But any decent modern engine should be enough to do a game like this, so it's up to you to choose one you like. Unity and GameMaker tend to be popular choices for beginners.

Really depends on what you're comfortable with. Without writing any code, I think this game could be a bit difficult to do, depending on what you're aiming for. Do you have programming experience? If so, what languages?

If you don't have any programming experience at all, I would recommend to learn the basics at least, before diving into any project. While it is technically possible to make a game without writing code, it does at times limit you and at times, may even be more challenging to accomplish than the coding itself (provided you know how to code).

Popular engines these days though for many are Unity, GameMaker, and Unreal. Again, just pick something you're comfortable with using. There isn't a strictly right or wrong answer, just benefits and drawbacks between engines, and many engines, you'll find, are roughly similar for most projects. 

I actually wrote a brief article with some "no code" options just the other day that might help give you an idea of some popular options:

Most of the listed engine have some form of free trial or limited free edition - I'd suggest trying a few out and picking what feels most comfortable for you.