Sorry to hear that you lost your notes and your older iTunes backup. I wish that iTunes retained a number of older backups rather than deleting them when a new one is made. I only see one possible option for you at this point but in order to try this, your lost notes must be extremely important, so important that you are willing to go through a lot of trouble to get them back. Think carefully before attempting the following. I personally do not have anything so valuable on my iPhone that I would be willing to do the following myself. If I had such documents I would have emailed them to myself or otherwise backed them up independently of iTunes.
Do you have a Windows PC? If so, have you made Windows backups in the past, either automatically on a schedule, or manually on demand? If you have, do you have a Windows backup predating the date when your notes were lost? If you have such a backup you can restore it or attempt to restore individual files or folders from it. This older backup would contain the iTunes backup file made at that time. You could then replace your newer iTunes backup file with the older one made prior to the notes loss. I have not attempted this nor am I likely to do so - it is possible that this may not work at all as restoring an older iTunes backup may not function properly in iTunes if iOS changes prevent it from doing so. Then again, it is possible that the older backup will indeed work. By first deleting the current iTunes backup and then restoring the older one through Windows, you could in concept get your notes back. If you have made Windows backups in the past read the articles below. They are for Windows 7 but similar articles exist for other versions, just select from the upper right corner of the webpages that ensue. Additional links are provided within those articles which could lead you to other choices. This is a lot of trouble worth it only in case of extremely important data and of course only available if Windows backups exist in your computer or an external hard drive. Good luck...
http://windows.microsoft.com/en-us/windows/back-up-files#1TC=windows-7
http://windows.microsoft.com/en-us/windows/restore-files-backup#1TC=windows-7
