Peace be upon you. It is not permissible, with a strong obligation to avoid it, according to Ayatollah al-Uzma Sayyid Sistani (may Allah protect him). As for Ayatollah al-Uzma Sayyid Khamenei (may Allah protect him), he states that it is not permissible for them to enter mosques at all, and the holy shrines are included in this ruling, with a strong recommendation to avoid entering them altogether. May you be successful in all good.