ETOPS 773 - As your PPL is only valid for aircraft up to 5700kg certified for single crew operations, the I offer you two points. As stated before, a sim engineer is not qualified to sign off flight training, (This has to be done by a Synthetic Flight Instructor/TRI or TRE ) and as the B777 is a) over the weight classification, and b) a two crew aircraft, then I regret that you are unable to log the time officially, for any hours consideration. However, write it into the logbook, for the memeory, and the experience. There is nothing to stop you doing that, and even getting it signed off by the engineer too. Just that its un-countable.