How would you recommend to schedule a task such as create and maintain project plan which applies regular weekly updates for the duration of the project?
There is a concept of BAU or CDB. That is "Business as Usual" or "Cost of Doing Business". In official PMI speak, it is called "Monitoring and Controlling". These are tasks and activities that need to be done and yet have nothing to do with the actual project.
For example, we have staff meetings every week, we don't task these out in a project. It's part of an overhead.
Creating a project status report falls into this category. It is part of the normal day to day function of the job.
If you are running an agile project, all these "Cost of Doing Business" items are just things you need to take into account when determining how much capacity you have to work. If the project status will take you four hours a week, your capacity is four hours less (Pro Tip- Capacity is NOT 40 hours. Average team capacity is about 20-24 hours a week).
If you're in a traditional project I recommend having a separate "project" which is your "Project Management Project". In here track all the things you have to do every week as part of your "day job."
You could use a hammock task and assign yourself to a low assignment unit (<5%). See: https://support.microsoft.com/en-us/kb/141733
The link references Project 2003 - but the same applies to later versions of project.