Thanks to the people in the comments i made it work.

The queries linked by @ThomA gave me NT AUTHORITY\NETWORKSERVICE as the user that was used in order to access the files.

SELECT value_data
FROM   sys.dm_server_registry
WHERE  value_name = 'ObjectName'
AND     registry_key = 'HKLM\SYSTEM\CurrentControlSet\Services\MSSQLSERVER'

OR

SELECT DSS.servicename, DSS.startup_type_desc,
       DSS.status_desc, DSS.last_startup_time,
       DSS.service_account, DSS.is_clustered,
       DSS.cluster_nodename, DSS.filename,
       DSS.startup_type, DSS.status, DSS.process_id
FROM   sys.dm_server_services AS DSS;   

Since my PC is set to german, i translated it to Netzwerkservice and gave access to that user(group) by following the steps described here. This solved the issue i was having.

Since your SSMS might be configured differently, i would suggest running the querries on your own setup again.

Alternatively:

Although it was not applicable to my case, if you can place the assembly file on your server directly the suggestion by @siggemannen is also an solution, since this removes the need to provide access to the user:

"Run: select * from master.sys.sysfiles and just put your files into the folder where master db is

However i cannot garantee that this is considered best practice