Your site column is deployed to the Site Column Gallery in a site. So first you need to get a reference to the site (i.e. an SPWeb object), then you get access to the site column using the Fields collection. Generally you pass the internal name of the site column as a parameter.
When you define the site column using CAML you set the following attributes: Name, DisplayName, and StaticName. The Name attribute is the internal name. It gets set when the site column is created and does not change over its lifetime. You could reference the site column using its ID (as you did in your question) but it makes your code unreadable.
Once you have the site column, you need to cast it as an SPFieldChoice and then you can get the choice values from the Choices property.
var web = SPContext.Current.Web;
var deptField = web.Fields["<internal name">"] as SPFieldChoice;
var values = deptField.Choices;