Due to notarization requirements, currently you may face issue while opening Visual Studio code on MacOS Catalina. To resolve this, go to

System Preferences -> Security & Privacy. Click the lock to make changes -> Provide your password. You’ll get a notification at the bottom that the “App was blocked from opening because it is not from an identified developer”.

click ‘open anyway’.

Check the screen-shot below:

This would open Visual Studio code on your Mac.

Here is the Visual Studio Code Requirements Page:

https://code.visualstudio.com/docs/supporting/requirements

Here is the Apple notarising documentation:

https://developer.apple.com/documentation/xcode/notarizing_macos_software_before_distribution