What is the smallest manned aircraft with four engines?
I present you Yves Rossy's Jet wingpack, which satisfies your conditions (I know I'm pushing it, but couldn't resist).



Yves Rossy's Jet wingpack, By Rama - Own work, CC BY-SA 2.0 fr, Link

It is certified by FAA as an aircraft, powered by four Jetcat P400 turbojets, piloted by an individual, not a rotorcraft and used in show business.

According to the official site, it weighs 150 kg.



@ymb1's logic is correct. To get to lightweight four engined aircraft with, you have to go back when the engines were not powerful enough for large aircraft. So, I present you the Sikorsky Ilya Muromets, the World's first four engined bomber. 



Sikorsky Ilya Muromets, By www.cultinfo.ru, Public Domain, Link

The Ilya Muromets Type S-23 V is reported to have an OEW of around 3700 kg, powered by four Sunbeam Crusader engines. Its predecessor, the Sikorsky Russky Vityaz, was still lighter, though it never saw service in numbers, sadly.

Of course they are not autonomous as per your requirement. Why would you want a manned autonomous aircraft anyway?