MX Plan : mailbox full and inaccessible, can it be restored ?

**I have a full mailbox which I do not have access to**

The 5GB quota has been filled up because the mailbox was not consulted for a long time. The quota is 5GB and the manager says that it has reached more than 6GB.

This mailbox is currently not accessible, neither via web, nor via IMAP.

This is the message I get from the webmail :

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I would be happy if I could remove some email and go on using this mailbox, but I'm wondering if this is possible, or if the mailbox is condemned. Since I cannot access it, I can't read the warning messages that were probably sent to the mailbox.

Strangely enough, the emails are still accepted.