As a lead developer on a team, how do you manage to stay productive ?

I am currently facing issues in my current job, I have been promoted (2 months ago) to lead developer in my team and got the following workload added :

• Plan with the project manager who will work on what
• Write technical specifications of projects
• Participate in functional specifications with clients
• Manage servers used by our team projects
• Sit down with coworker to resolve problems they are facing in their code
• Review code produced
• Automate process to increase team productivity
• R&D for our apps and backends
• Create processes to ensure the quality of our production

But meanwhile, management expects that I keep producing at the pace I was before the promotion. In my planing I have no dedicated tasks for these parts:

• Plan with the project manager who will work on what
• Sit down with coworker to resolve problems they are facing in their code
• Review code produced
• Automate process to increase team productivity
• R&D for our apps and backends
• Create processes to ensure the quality of our production

So for the last two month, I have been putting the hours to meet their expectation of my productivity, while doing the tasks above.

I have already raised this issue to my management, but things do not seem to change.

I would like to know how more experienced Lead developer would deal with this, and if you have some advice along the way, that would be really nice!