You shouldn't have two checkboxes with same name, in same form. You have two checkboxes in your HTML, 1 for yes and 1 for no. Surely you just want a single checkbox that means 'yes' when checked and 'no' when left blank?
Presuming you remove the duplicate checkbox, so you have a single checkbox called 'spec', when the form is submitted, if 'spec' was checked, you will have a POST / GET variable called 'spec' (e.g. $POST['spec']). I can't remember what the contents of this var will be, but it doesn't matter. If the checkbox was not checked, the $POST['spec'] (or $_GET['spec']) will NOT be set.
So, you just need to determine if the $POST / $GET 'spec' variable exists after form is submitted. If yes, set your enum column to 'Yes', if no, set your enum column to 'No'.
Does this make sense?