Whose gate is it?

[SC Ump]

In the pregame, the home team coach covers the ground rules including the statement, "There's gates next to both dugouts that we need to keep closed." During the game, the home team has left their gate open and an overthrow by the visiting team goes out the gate.

Normal deadball and advance runners? Deadball and apply "offensive blocked ball rules"? What say y'all?

(I'll tell you what we did later.)