How to minimize chrome browser to tray when I click on standard minimize button?
I don't want Chrome to appear in task bar.
Can we implement this by Chrome extension code?
As amer pointed out, there exists an extension solely purposed to do this functionality.
Luckily, the extension is open source and has a home here you can borrow it as long as your extension itself is kept open source (you should check the license for details).
Note, though, that since the chrome extension APIs don't provide this functionality (tray icons and hiding browser windows), the extension resorts to an NPAPI plugin (you can see in the source trunk that it bundles a .dll file, and that is open source (C++) too!).
It's not the best case scenario, Google discourages NAPAPI unless it's the only way (in this case, unfortunately, it is) due to security openings. The extension on the Chrome Web Store will ask for permission to "Access your data on your computer" which is seen negatively by wary users, especially and justifiably so if you don't take an effort to explain that general permission wording more clearly in your extension description.
Also the extension is targeted at Windows platforms, so you would have to look into specific NPAPI implementations for Linux and Mac if you need to support them.