What does it mean "the airport has the code A 129" (Nida airport, Europe)?
This is really just an educated guess, but it sounds like it was assigned that identifier by the Lithuanian civil aviation authority. It obviously didn't warrant an IATA code. Since it was closed to most traffic the ICAO code may not have been in use. The wiki page said it was just considered an "airstrip," so it was assigned an ID by the government. (It also mentioned lack of fuel service. That might be a requirement for an ICAO registration. I don't know.)

Here in the US large airports will have an IATA CODE, an ICAO code and an FAA location ID. [example: O'Hare airport - IATA: ORD - ICAO: KORD - FAA: ORD] A small GA airport won't merit an IATA or ICAO code but it will have an FAA location ID. The small airport near where I work has no IATA or ICAO code. It has the FAA location identifier K68.