Yes you can not carry on the grounds of any School.
There are exceptions which may apply in your case.
(4) says you can carry if you are dropping off or picking up passengers as long as you remove or use or allow the removal or use of the weapon.
(c)(1) the second half of which says....
"It is not an offense under this subsection (c) for a nonstudent adult to possess a firearm, if the firearm is contained within a private vehicle operated by the adult and is not handled by the adult, or by any other person acting with the expressed or implied consent of the adult, while the vehicle is on school property."
There is not complete agreement on what 39-17-1309(c)(1) means when you look at all of 39-17-1309 on all the gun boards I am on.