It is many years since I`ve gone to the ferry port at Barca, so listen to anyone else who has been recently, but I would ignore the satnav and look for signs.
A9, Badalona, and down the Litoral.
Almost certainly the weight limits will be except for access, and no way would I try to dodge the signs and go through the town.
Confident smile, and just keep going… 
Dont worry too much, weight limits arent capital offences.