Does using the Tavern Brawler feat with a rope give you a 20’+ grapple attack?

If I gain the Tavern Brawler feat, and use it with a rope as an improvised weapon, can I initiate a Grapple at 20+ feet away (depending on the length of rope)

When you hit a creature with an unarmed strike or improvised weapon on your turn, you can use a bonus action to attempt to grapple the target.

So as an action I attack by whipping the rope out, presumably doing 1d4 damage + strength (up to the DM). Then as a bonus action I initiate the grapple by tugging the rope and having it wind around the opponent.

I envision this as a lasso, but I suppose a grappling hook would work too.