Perhaps weather fax or other data?
USCG SITOR out of NMF Boston has been logged on that frequency as recently as June (by another DXer, not myself), although the USCG site doen't indicate 6360 KHz as being used.
I've just picked up something (@ 1455 UTC) on their listed frequency of 6314. A short high-pitched tone, followed by the rapid morse code you've talked about. Clearly data transfer.
BG