Thank you all for helping with my problem.
After browsing the internet, I found several threads about audio on Asus Laptops. It seems that currently there is no sound in Linux when using Asus Zenbook laptops (links 1 2). Possibly, Asus can fix it via a new BIOS update link. This problem can be fixed on some models via different hacks (for example this Reddit thread). Some users succeeded when using custom kernels and quirks (although there already are some audio quirks in the kernel for different Asus laptops). Unfortunately, there is no quirk for my model, UX582HS.
There was an article about word sniffing from windows to get the correct parameters for the audio card via hda-verb link. If I understood the forums correctly, performing all the manipulations and getting the correct hex-values for hda-verb may help. But I think that it is too complex.