How do I save updated container?

I updated Docker container.
How do I publish it?

You can use the push step to push any container to your registry.

I assume that by “updated” you mean you changed the dockerfile. Or do you mean something else?

Not dockerfile.
Container.

You can use the docker save/export commands.

However, you won’t normally use these commands with Codefresh

Can you explain a bit what you are trying to do and what is your use case?