For the first time in history, this the author worked with two digits bordered magic squares multiples of 4. These are from orders 8 to 40. These can be accessed at the following links:
1. Two Digits Bordered Magic Squares Multiples of 4: Orders 8 to 24.
2. Two Digits Bordered Magic Squares of Orders 28 and 32.
3. Two digits Bordered Magic Squares of Order 36.
4. Two digits Bordered Magic Squares of Order 40. (This work)

The work is for the order of type 4k+2, where k>1, i.e., for the orders 10, 14, 18, 22, 26 and 30 can be access at the following links:
1. Two digits Bordered Magic Squares of Orders 10, 14, 18 and 22.
2. Two digits Bordered Magic Squares of Orders 26 and 30.

In this work we shall give two digits bordered magic squares of order 40. As explained in previous works below is digit-wise classification of bordered magic squares:

Single Digit: Bordered magic squares based on single digit.

Two Digits: Bordered magic squares based on magic rectangles of order 2xk (k=4, 8, 12, …).
Three Digits: Bordered magic squares based on magic squares of order 3:
Four Digits: Bordered magic squares based on magic squares of order 4.
Five Digits: Bordered magic squares based on magic squares of order 5 (appearing soon).
Six Digits: Bordered magic squares based on magic squares of order 6, etc.

The work can also be accessed at the following link:

Inder J. Taneja, Two digits Bordered Magic Squares of Orders 36 and 40, Zenodo, May 04, pp. 1-41, 2023, https://doi.org/10.5281/zenodo.7896709.
Below are few examples along with pdf file of order 40 for download.