In Firefox, to access the HTML version of your code, select your text and then right click and select View Selection Source. In the window that pops up, your HTML text is already selected. Copy that.
Now how to send it from Gmail? This is a problem with Gmail, not TW. But someone has worked out a neat solution using Google Docs/Drive. Read it about it here:
http://www.labnol.org/internet/send-html-email/19672/Once you have installed the spreadsheet in Google Drive you will be able to open a form that lets you paste in your HTML code and send it.
Not a one-click solution, but better than doing all that formatting by hand.
Another solution, if you have a desktop client like Thunderbird hooked into your Gmail, is to just send from that client. Thunderbird has an option to insert html.
Good luck,
Mark