Restoring oracle database
Can you copy the 11.2.0.4.0 rman executable from your friend or get and perform a second "dummy" installation of Oracle Database on another temporary computer/server? If so, here's how you can solve it:

Let's say you were able to copy the 11.2.0.4.0 ORACLE_HOME folder from your friend, and called it dbhome_2 (do not replace current, otherwise you can mess up things).

Using the 11.2.0.4.0 rman executable:
- startup instance in nomount and restore controlfile from backup
- mount the db
- restore the archivelogs required (recover database until cancel)

Shutdown the database, and using 11.2.0.2.0 executable:
- restore the control file again, from a 11.2.0.2.0 generated backup
- mount the db
- recover database until cancel
- open database with resetlogs

Hope it helps.