AlexandrP, with priv-lvl = 15 you must be logged as an admin "#". You must have a mistake in your TACACS+ user config.
The examples I gave above were for TACACS+ running on a Ubuntu server and are working. The "Stef" user has admin privileges, the "Blackdiamond" user has only read-only access (>) and some commands are unavailable (like "sh edp").