So in effect the "code" is fixed for each route, that's useful for passengers as a "route number"
The 4 digit PIS code is fixed for that specific combination of Origin, Destination and Calling Pattern, but I wouldn’t say it’s useful to passengers, no -
1) because even for a given route the different options can have wildly different codes; for example the Reading to/from Gatwicks could display externally any of 03/10/11/12/13/14 depending on calling pattern, origin and destination.
2) there is significant overlap in the database of codes - so for example the “10” from above might appear on the North Downs, or on any of the Marlow, Henley or Greenford Branches, plus also on various versions of Paddington to Didcot/Oxford stopping services. So which is your “Route 10”? Marlow, Henley, Gatwick or Oxford?
3) on a similar vein, even within a route, the codes are relatively meaningless - a train will show “03 Gatwick Airport” if it’s calling all stations or Wokingham - Guildford - Redhill only.
4) Their meaning is not advertised to the public anywhere - it’s just a quirk of the hardware on the train that it displays the first 2 digits of the code on the screen. What information do they additionally convey that isn’t already on the info screens on the platform, in a much easier to digest format for Joe Public?
As to a full list; the code books are internal documents marked “private not for publication” so cannot be shared.
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Yes, in the days before widespread platform displays and automatic announcements it was useful that the train itself showed where it was going and how it was getting there - that’s why most of the Southern Region slam door stock had number blinds on the front and the meaning of those numbers was published in timetables. Nowadays there are better ways of conveying the same information so they’re no longer necessary, and modern trains have done away with them.
It’s just the Hardware on the Turbos hasn’t been updated to do away with that capability so shows a meaningless number next to the destination.