HEX EDITOR FIND A REPAITING SEQUENCE OF BITES

I have a binary linux file. There is a secret key in it that we can find in a HEX editor. The key is in HEX format. I know that the key consists of 16bytes or 32 characters. what else i know is that it is 8bytes + 8identical bytes. I would like to find a hex editor that can find this pattern. I don't know anything about the key only thing i know is what i described. eg the key is AABBCCDDEEFFGGHHAABBCCDDEEFFGGHH as u see the 16char are repeated once that is the key. Could this be achieved by writing a bash script? THanks