With the SYS user you should be able to use the "Enable Enterprise Geodatabase". However, you should assign the required package privileges before. Connect to Oracle with SQL*Plus using SYS, and execute the following:
GRANT EXECUTE ON dbms_pipe TO public;
GRANT EXECUTE ON dbms_lock TO public;
GRANT EXECUTE ON dbms_lob TO public;
GRANT EXECUTE ON dbms_utility TO public;
GRANT EXECUTE ON dbms_sql TO public;
GRANT EXECUTE ON utl_raw TO public;
Privileges for geodatabases in Oracle—Help | ArcGIS for Desktop
Please provide a screenshot of the connection properties as Asrujit suggested.