non archived courses should be preferred

courses/models.py

@@ -569,19 +569,25 @@ def active_products(self):
     @cached_property
     def first_unexpired_run(self):
         """
-        Gets the first unexpired CourseRun associated with this Course
+        Gets the first unexpired/enrollable CourseRun associated with this Course. Giving preference to
+        non-archived courses
 
         Returns:
-            CourseRun or None: An unexpired course run
+            CourseRun or None: An unexpired/enrollable course run
 
         # NOTE: This is implemented with sorted() and courseruns.all() to allow for prefetch_related
         #   optimization. You can get the desired course_run with a filter, but
         #   that would run a new query even if prefetch_related was used.
         """
         course_runs = self.courseruns.all()
         eligible_course_runs = [
-            course_run for course_run in course_runs if course_run.is_enrollable
+            course_run for course_run in course_runs if (course_run.is_enrollable and not course_run.is_past)
         ]
+        if len(eligible_course_runs) < 1:
+            # check for archived courses
+            eligible_course_runs = [
+                course_run for course_run in course_runs if course_run.is_enrollable
+            ]
         return first_matching_item(
             sorted(eligible_course_runs, key=lambda course_run: course_run.start_date),
             lambda course_run: True,  # noqa: ARG005