Add your cylinder, and make it the proper size for the baseplate.
After that go ahead and add another cylinder. Go into edit mode (Press Tab), select all vertecies with A and then move the cylinder out to the first hole position, and scale it properly. Exit Edit mode when you're done. Your thing should look like this now.
Add an empty next. (Shift A -> Empty and select whatever you want). Select the small cylinder now, and go to the modifiers tab. This will be on the right hand menu and looks like a wrench. Hit "Add Modifier" and select "Array". Uncheck "Relative Offset" and check "Object Offset". Set your empty as the object, and set the count to whatever you desire. This is what the modifier should look like.
Select your empty again, and rotate it around the Z axis by 25.7° (Hit R, then Z, then type in 25.7). Leftclick when you're done. After that select the big cylinder again, and add a boolean modifier. Set the type to "Difference" and in the objects section select the small cylinder. If you're not happy with the positioning at this stage you can move the small cylinder around in edit mode to get it lined up properly. Hit "Apply" on the boolean modifier of the big cylinder when you're happy. You can delete the small cylinder and the empty after that, if you want to. This is what I'm left with.
To recap what we've done: We've taken a small cylinder, and copied it 13 times (that's the count in the array modifier). After that we've told blender to offset it based on an object, and selected an empty for that. We've rotated it by a desired angle, and the small cylinder copied that angle as well. After that we substracted the small cylinder from the big one and are left with the final product.
