Hello Dani,
I'l try to help you.
Empty Weight: 167T (ER version)
Fuel: 7,5T/H 7,5*6=45 + landing with the same (7T) FOB=53T
Pax: 2 class is 435... average weight no charter flights is 84 kg for adults...
and baggage 15kg for intercontinental flights... 99kg per person
99*435= 43T
TOW: 263T
And then look at this document: ( choose airplane performance)
Boeing: Commercial Airplanes - Commercial Aviation Services - Flight Operations Support - Airport Technology - 777 Airplane Characteristics for Airport Planning
You can there see that you need a runway that is around 5400 ft long (1650m)...
So your 2300 m are enough
Hope it helps,
//Robini