First, I’d recommend using single-quotes around the variable itself … makes it easier to preserve double-quotes in the actual HTML code.
You can use a backslash to separate lines if you want to maintain a sense of formatting to the code:
var code="<div class="my-class"> \ <h1>The Header</h1> \ <p>The paragraph of text</p> \ <div class="my-quote"> \ <p>The quote I\"d like to put in a div</p> \ </div> \ </div>';
Note: You’ll obviously need to escape any single-quotes inside the code (e.g. inside the last ‘p’ tag)
Anyway, I hope that helps someone else that may be looking for the same answer I was … Cheers!