Hi,
I do see 04 (I'm the guy mentioned above) but only in certain situations. If your booting up from a cold then you shouldn't really see 04 although it isn't actually an error code.
In my case 04 relates to a power state. Windows 8 has a function called 'Fast Start up'. This creates a folder which saves all your settings on shutdown. If you boot back up again relatively quickly then Windows uses this folder to boot faster and the 04 code will then appear. This is much like resuming from sleep where the code 03 will be seen.
Turning off Fast start up via the control panel and power options will see the system boot up from stand still with no 04 code and it will boot straight to A0 as per normal function.
In your case booting from cold you should see A0 or whatever stands for normal operation with your board although your motherboard may differ from mine (GA-Z97X-Gaming 7).
If your system is running without issue i wouldn't worry about it. If it does bother you though you could try reseating your components like gpu, ram and HDD.