Servo, try Qatar Airways, they are hiring non-type rated captain on the widebody. This is what I found on their website for Widebody captain position.
Total hours 7000.
Minimum 2000 hours in Command on Multi-Crew, Multi Engine Jet Aircraft in excess of 100,000kg MTOW.
Valid ICAO ATPL
Valid instrument Rating
Valid Class 1 Medical.
ICAO English Proficiency Minimum level 4.
*To be eligible for a direct entry Captain position, candidates must be currently flying as Captains
I am sure you meet all the conditions above so you might have the chance to get the 777 .First, call their HR to see what they are saying about your case and then try talking to few Qatar pilots here.
All the best