Trixie Belden and the Mysterious Code (1960)
Trixie Belden and the Mysterious Code is a 1960 trixie belden (fictitious character) book written by Kathryn Kenny.
When the Bobwhites take a week-long vacation on Cobbett's Island they find that their vacation house has a hidden story. Will the Bobwhites be able to solve the mystery before it's too late?
Linked book is actually Mystery on Cobbett's Island, as per the cover pic, not The Mysterious Code as in the title.