I mean the best way to earn that amount of nTP would be a RTW trip, I've managed to build an itinerary which earns 20k with 3 continents, but 28k should be possible if you do a 4 continent one, and starting in Oslo (cheapest place to start) that should cost around £5.5-6k incl taxes, plus some hotel costs and the positioning flight to OSL. Others on the oneworld forum have done the same too.

But that doesn't give you the 20k that you need to get on BA. It's unclear whether BA uses revenue based earning on RTW tickets ticketed by another OW airline (might have been figured out by now, I've not checked for a while tbh), but if not, and RTW tickets credit based on distance, BA flights would give 50% of miles flown, and so doing a LOT of the trip on BA would get you at least close.

Just looking quickly, if you did a RTW starting in OSL, and then go OSL-LHR-DXB-LHR-SCL all on BA, and then some more flights on other OW airlines though north america and asia to rack up the other 8000nTPs, but ending in SYD, and then going SYD-SIN-LHR-JNB-LHR-OSL all on BA, that is 36k miles on BA, which would be 18k nTPs, so gets you most of the 20k you need with a 6 continent RTW. There are probably BA codeshares in NA and Asia which you could add to rack up some more BA points too, and if you can find enough you may be able to drop a continent to reduce cost too. I believe that is a valid RTW itinerary but havent checked it fully, and this does rely on BA flights on a RTW crediting as distance based, which I'm also not sure of. But if BA flights on a RTW which is booked through a non-IAG airline credit based on distance, this would for sure be the cheapest way to do it.