There will be 2 case for the string of length 2014 :
Either,
1) It will be halt on final state i.e. accepted.
or else,
2) It will halt on non-final state or go on a loop.
So this is a partially decidable language.
If 100% decidable then Recursive
If partially decidable then Recursively enumerable
If 100% not decidable then not Recursively enumerable
Hence it is Partially decidable(Undecidable) and Recursively Enumerable.