I don't believe they did, or have any intention to do so. BA is unlikely to have many traffic rights to sell standalone codeshares on TPAC routes anyway; if they existed it would probably be in conjunction with a flight from London.
There used to be a random codeshare on JL (I think it was JFK-NRT) but there were never any sensible fares filed to make it usable (except perhaps as part of a RTW).
There also used to be codeshares on QF flights to Australia out of LAX, but they were either only bookable in conjunction with LHR-LAX flights, or again, the fares didn't make sense.