Though there is no specific log code for what you are looking for...
Perhaps we can narrow it down...
a) This code is under the 10,000 code thus is a CORE Framework ArcGIS Server error
b) All codes in the 9-xxx (nine thousands) seem to relate to Service Requests type errors.
Is there some specific request that correlates to the time at which you receive the log code?
I get 10 or more logs like this one every 3 or 4 min, I cannot relate it to a specific request:
<Msg time="2016-03-22T13:48:09,770" type="WARNING" code="9516" source="Soap" process="18232" thread="35" methodName="" machine="XXX.XXX.XXX.XXX" user="" elapsed="">Tile (layer=_alllayers,mapname=Layers, level=12, row=131,560, column=83,617) could not be found.</Msg>
Checking PID 18232 : javaw.exe
Tile (layer=_alllayers,mapname=Layers, level=12, row=131,560, column=83,617) could not be found.</Msg>
Looks like an issue with your cache level 12. Is it possible for you to rebuild/create that level?