You can switch a project to code first and generate the scripts you need via migrations. See the link below for a guide on moving from db first to code first, but it sounds like you may be partially there already.
enable-migrations for the project with your context if you haven't already.
2) create a baseline migration. EF will use this as a starting point so you won't get a bunch of code to create the objects that already exist. The ignore changes flag tells EF not to create the existing objects. https://msdn.microsoft.com/en-us/data/dn579398.aspx?f=255&MSPPError=-2147217396#option1
create-migration InitialCodeFirst -IgnoreChanges
3) Now modify your schema as you normally would and create a migration:
4) Create a script for a different database (like PROD) by using -Script. This will not update your database it just creates a script, so I usually run it a second time without -Script:
update-database -Script // creates a script (in VS), but does not apply update-database // updates the database your connect string points to
5) DBA runs script and this will add a record to __MigrationHistory to identify it as being applied.
Here is a useful link on deployment: http://cpratt.co/migrating-production-database-with-entity-framework-code-first/#at_pco=smlwn-1.0&at_si=54ad5c7b61c48943&at_ab=per-12&at_pos=0&at_tot=1