2000 is basically 'no transponder code assigned'
Transponder Modes and Codes
2000 — Oceanic
[ICAO Doc 8168, Vol I, §III-3-1-1, ¶1.1.2] Except in case of emergency, communication failure or unlawful interference (see 1.4, 1.5 and 1.6), the pilot shall:
a) operate the transponder and select Mode A codes as directed by the ATC unit with which contact is being made; or
b) operate the transponder on Mode A codes as prescribed on the basis of regional air navigation agreements; or
c) in the absence of any ATC directions or regional air navigation agreements, operate the transponder on Mode A Code 2000.
[ICAO Doc 7030, §AFI, ¶5.1.1.2.] Africa-Indian Ocean Regional Supplementary Procedures. Unless otherwise directed by air traffic control, the last assigned SSR (Mode A) code shall be retained. If no SSR code has been assigned, Mode A code 2000 shall be selected and retained.
[NAT Doc 007, ¶6.8.1] All aircraft operating as IFR flights in the NAT Region shall be equipped with a pressure- altitude reporting SSR transponder. Unless otherwise directed by ATC, pilots flying in the NAT FIRs will operate transponders continuously in Mode A/C Code 2000, except that the last assigned code will be retained for a period of 30 min after entry into NAT airspace or after leaving a radar service area. Pilots should note that it is important to change from the last assigned domestic code to the Mode A/C Code 2000 since the original domestic code may not be recognised by the subsequent Domestic Radar Service on exit from the oceanic airspace.
[AC 91-70A ¶5-5.b.] In airspace controlled by Oakland Center or Honolulu Center, accomplish normal VHF communication. In airspace controlled by Oakland Oceanic (KZAK), CPDLC or HF voice backup accomplishes ATC communication (including en route requests) and position reporting. You can also use HF as primary communication for the aircraft not equipped with data link. When reaching oceanic airspace, squawk 2000 and monitor VHF 121.5 and the pacific air-to-air frequency 123.45.
[AC 91-70A ¶8-16.b.] In South America, there are no alternate instructions in the AIP. Therefore, use code 2000 when beyond radar coverage if there is no specification for another code.
[AC 91-70A ¶13-9.b.] Special Requirements For Flights Transiting Iceland. Pilots will operate SSR transponders continuously on Mode A, Code 2000, except that departing aircraft will retain the last assigned code for 30 minutes after entry into NAT oceanic airspace unless otherwise instructed by ATC.
[AC 91-70A ¶14-2.d.] On polar routes beyond areas of radar coverage, squawk 2000.
[AC 91-70A Appendix 2, ¶2.g.] Thirty minutes after oceanic entry, crews should Squawk 2000, if applicable. There may be regional differences such as Squawking 2100 in Bermuda’s airspace or maintaining last assigned Squawk in the West Atlantic Route System (WATRS). Crews transiting Reykjavik’s airspace must maintain last assigned Squawk.
In general you are going to squawk 2000 when oceanic, waiting 30 minutes after the entry waypoint is required over the North Atlantic and doesn't hurt elsewhere. There are exceptions so make sure you view the regional pages before entry.