The code AXJ in relation to Sri Lanka most likely refers to flights from Amakusa, Japan (AXJ), to Sri Lanka. Several travel and flight search websites use the airport code AXJ to identify routes that fly to destinations in Sri Lanka, such as the capital, Colombo (CMB).
Amakusa is a city and region in Kumamoto Prefecture, Japan. Therefore, the connection is between a specific Japanese city and the South Asian island nation of Sri Lanka.