Hi there!
I will be happy to help you with that. Unfortunately, Google Docs don't have onEdit trigger like Google Spreadsheets, which will allow us to catch text inside quotations while you are typing, but we have a solution for that.
I will provide you with two ways to call the script. If you are trying to highlight quotations in an existing document, then you will call the script using a custom menu.
If you want to highlight the text as soon as you type it, we have a tricky solution for it using a sidebar.
Both approaches will be provided to you and then you can make your choice. I will be happy to address any of your questions!
Sincerely,
Mohamed