A rode is a nautical term for a rope, especially one used to secure an anchor, or trawl. (Oxford Dictionaries). The term is marked as NORTH AMERICAN.
From the OED.
N. Amer. regional (chiefly New England and Newfoundland). Naut.
A rope, esp. one attached to the anchor of a boat. Cf. roding n.3
Note that the OED mentions nothing about trawl. But it gives examples from 1612, the most recent ones being:
1963 J. T. Rowland North to Adventure x. 147 With both hooks down
and a long scope of rode she should be able to ride out anything.
1986 J. Feltham Islands of Bonavista Bay 55 On the fishing
grounds, the motor boats, like the bullies, were moored with ‘rodes’
1996 Chesapeake Bay Mag. Sept. 37/2 Carry a good anchor with
plenty of chain and rode.
So the OP's fishing rode would seem to have some connection here.