If you're playing MP than you can't use the jump gate, it'll just say "Access Denied." But as far as getting through the mine field just keep following it, you'll eventually find a huge gap. Someone somewhere isn't a very good mine layer ^_^. To help you locate it just a bit you should be just about perfectly lined up with the front of the gate when you find the gap.

You can't enter the gate in SP either except during one of the campiagn missions

If you still want to enter the minefield there are several threads called "Zone 21", "Alaska", "Minefield" or something like that. Basically, take the trade lane from Norfolk Shipyard to Texas Jumpgate, leave it just in front of the 3rd ring (enter free flight), about 16k from Battleship Missouri, then head directly for the "Unknown Jumpgate" and you'll pass the minefield through a small tunnel.