If you are interested, then
I've temporarily disabled (unchecked) "Block vulnerable kernel drivers" in Avast -> Menu -> Settings -> General -> Troubleshooting -> Enable Self-Defence (to prevent blocking of the vulnerable driver).
And I've found the Software which uses this driver via Process Explorer (File -> Show Details for All Processes) -> Find -> Find Handle or DLL (Ctrl+F) -> in "Handle or DLL substring" typed "WinRing" -> Search

In my case it was PCMeterV0.4.exe which is extension for Windows 7 Gadgets "All CPU Meter" / "GPU Meter" (uses file "\Device\WinRing0_1_2_0").
And this is pretty logical that this software tries to get access to hardware via kernel drivers to monitor the states of the CPU/GPU which could be identified as mining software...
Next step, I'm planning to play with the check boxes in PCMeter settings, to partially disable it or I'll remove PCMeter in case if nothing help.