As far as I know there is no way to pull info from the HTTP headers directly by using the Insert From URL script step.
If I was going to do something like that I would create a custom PHP page that would use cURL to send a request to the intended destination. cURL can tell you what the response code is, I believe there is even an option to follow 301 redirects. You could even use the Filemaker PHP API to write the status code to a record in the database.
Can you use a plugin? The free BaseElements plugin will (apparently) do the cURL work for you. First use a set field to Get the URL. Then use another set field step to get the code. The example below sets fields in a "Pages" table. (There's also a plugin function that gets the headers.)