NOTE: This solution will be spoiler heavy, only use for guidelines if stuck.
This is the second story related trophy.
It can be quite dofficult to figure out the code, which can be done by reviewing the documents you've collected from the West Wing.
After you've got the key from the library, head back to the Entrance Way, via the upstairs door in the library. Open the west wing doors and take the first right, to find Lara'a mothers hideaway, before you enter though open the cupboard to the right of the door for an document.
Explore every thing in here and you'll easily get the clues needed to progress the story. Make sure you climb the ladder and open the box and the door up top with the master key.
The game will ask you to move on to the Master Bedroom.
You'll find two clues in here.
You'll have a document that tells you how the code is broken down:
Lara's Expesition Treasure
Favourite painting by Amelia
Lara'a treasure is in the chest above the library (on the balcony). Heading to the desk down the back of the library will help you decifer the first number.
In Amelias room, you'll discover that his favourite painting gas red blocks, look at them to discover which on it is.
Their anniversary is learned in the Master Bedroom.
If you can't figure it out the code is 549 (5 - heiroglyphic number, 4 - Fourth painting along, 9 - October)