Leonardo - Press F-Key above F12?

For a project I'm working on, I need to use an Arduino Leonardo to make a button signal an external program. I can't directly add code to the program to make it pick this up, but I can make it pick up a key press. Because of this, I decided to just have a key get pressed by the Leonardo and pick that up in the program. I don't want the key to interfere with any typing function or the like, and the program supports f13, f14, and f15, so these are the buttons I want to press. Is there a way to do this? From looking at the number/key chart, I don't see a way to.

Note: I may have posted this in the wrong subforum. I apologize.

check - C:\Program Files (x86)\Arduino-1.5.8\hardware\arduino\avr\cores\arduino\HID.cpp

there is the function sendreport that send the actual keycodes, you could try to extend this keyboard class

in - C:\Program Files (x86)\Arduino-1.5.8\hardware\arduino\avr\cores\arduino\USBAPI.h
there are keycodes for F1..F12 you could make an educated guess what the F13..F15 could be.

Hope this helps

(adapt path to your version of course)