Ah, it's only the official aircraft types 'book' you can view online. ICAO DOC 8643.
The 'Designators for Aircraft Operating Agencies', ie. 3-letter airline codes is DOC 8585 and published quarterly.
The 'Location Indicators', ie. 4-letter airport codes is DOC 7910 and also published quarterly.
If you ask nicely, one of the many ATC workers on here might be kind enough to save you the last quarters' book for you and send it on?