Mounting heavy items with no studs
The rack is 28 inches wide. Its bound to be over at least one stud. How did you try to locate? Did you use a good stud finder? Look for hints for where a stud might be, like an electrical outlet below. (electrical boxes are usually mounted on a stud). Also a magnetic stud finder would find nails and screws. I would try again to find at least one stud and attach the rack to that with two screws, and use steel toggle bolts for the other two into drywall.