To add some more confusion:
which is usually the very best resource for a/p codes, lists "Saddam International" as SAD - fitting as it would be, I had so far only heard of SDA.
Problem is, SDA is Shenadoah/IA, while SAD is Safford/AZ.
Could it be BGW was the code for the main airport until Saddam came to power? After renaming Bagdad Intl, they could have given BGW to Al-Muthana (and continued using it as area code)?
Indeed very confusing.