Do you need Publix specifically? I don't know about a new Publix near Goodings--however, there is a new (within the last year or so) Winn-Dixie near Goodings. Turn right out of OKW. Go to the end of Community Drive and turn right again. Follow the Road to Hotel Plaza Blvd and turn or bear left onto Hotel Plaza. Drive down Hotel Plaza Blvd, turn LEFT at the traffic light. (If you drive straight across at the light youll be in Crossroads Shopping Plaza--don't do that.) Continue down the road, (you'll pass the Ale House on your left). Keep going--not far--and Winn-Dixie comes up on your right. It is set back a bit in a small shopping area. It is a lovely store.
If you turn right at the previously mentioned traffic light (at the end of Hotel Plaza), and drive down the road for a while, there is a Publix--on the left, I believe, but it's not new.
Give the Winn-Dixie a try. We were pleased with what we found there.