The Landing Climb Weight of a 777-300 with Trent 892 outside temp 50deg and QNH 997 is ~ 245tons, only corrected for pressure alt, not for density alt which would paint a more bleak picture .... (MTOW 299'370 / MLW 237'682)
The GA Climb Gradient is around 2%.
Having flown that bird many times in these conditions leaves me with some doubts about these values though .....