Do you use the camera calibrator app from MATLAB? This makes it easy to calibrate the camera.
The only thing you need to know of your checker board is the square size in the real world (in mm). It doesnt matter if you take a checker board picture from 1 m or 10 m distance, the real world size of the squares will always be the same, the rest is perspective of the camera.
If you have the camera mounted 10 m away from the plane you want to look at i would just make the square size bigger, in the matlab example its 29 mm, so maybe go with 50 to 100 mm for one square. Keep in mind that the checkerboard should be a odd number of width and height, and you should have at least 12 detectable points, so a board with 5x4 is your minimum borad size.