There's a way to discover the code you need to enter for the airplane
DISCLAIMER: You need dark element & lv. 500+ to preform this.
Bow to open the crowned royalty door
Run all the way up the stairs when you enter
Run through the elemental guards and go to the first painting you see
Use your dark fairy element to unravel the illusion, you'll see a bunch of wood infront of the painting on the floor
Pull out your hammer and jump on the wood while tapping/clicking
Once you walk down, walk straight until you find a room with a book in the middle
Once you find the book, in the upperhand corner you'll find 4 digits. copy and paste those randomized digits
Go back to castle heart
Go upstairs and in front of the fireplace
Enter the randomized code you got and climb up the tower [count the squares and enter the digits in CHRONOLOGICAL ORDER]
Fly upwards until you see the sky
Open the chest and tada!
Hope this helps [it's very short it only looks longer bc i hit enter so many times] it's very easy to engrain this into your memory if you ever wanna help people!