That's the afternoon ex-BOM service if memory serves right.
Should be a 777-200ER. 77C is not an official designation and I've never heard it before.
To above, BA does not have any 777 aircraft without WT+.
777 = 777-200
772 = 777-200ER
77L = 777-200LR
773 = 777-300
77W = 777-300ER