Tira here to help.
Are you looking to add notes in your Shopify admin for your discount codes? If you are, there isn’t a formal way to add notes to your discount codes, but you can use the “Timeline” located at the bottom of the discount’s page to leave any comments you have. When comments are added there, they will stay there and are viewable whenever you access the discount code's page. Comments can also be edited or deleted. Here’s a screenshot of the timeline from my test store:
To add to a discount’s timeline, you can follow our help doc for the steps here: Use the discount timeline.
Is this what you were looking to do? What would you use your notes to indicate? Let me know and I would be happy to take your thoughts to our developers so that they are aware of how we can improve Shopify for you and all of our merchants.