After posted this question, it turned out that mimics might be weaker than I though first.
As said in this linked question, I really like mimics and I'd like to use "a lot" of these (without going too far and make my players paranoiac) even when party level is increasing.
Also in the comments of the linked question's accepted answer, Erik told me that:
a basic Mimic probably won't ever challenge a high level party, but there are similar monsters of higher power levels, or you can make your own...
So I now have another question: How can I make mimics a real challenge for a high level party? Which monster would be similar to what a higher level mimic would be? (a party of 4/5 players)
I'd like mimic (or similar monsters) to be a challenging fight, maybe not deadly, but at least interesting fight, not over in less than two rounds. If necessary or easier, you can split the answer to address to floor level (i.e.: level 5 to 10, 10 to 15, 15 to 20, 20+).
As I'm very new to D&D (only started to buy basic rules, read linked question and this one for context) and even if I read a lot of this RPG stack Dnd questions, I'm not very aware of how to make changes while leave game balanced. So please be clear about how you managed to make it fit to another level (if so).
It also doesn't really matter if it's not RAW as long as it isn't game breaking.
Answers have to be based on prior experience about using mimics at higher level or at least using monsters at higher level than their basic one. If the answer is based on the use of these similar monsters, please back it with some in game experience about it, as a player or a GM, to support the fact that it's similar to a mimic.