Example 8 $n$ teams are to hold a home-and-away double round-robin match (each pair of teams plays two matches, each having one home match), and each team can play multiple away matches within a week (from Sunday to Saturday). However, if a team has a home match in a certain week, no away matches for that team can be scheduled in the same week. If all matches can be completed within 4 weeks, find the maximum value of $n$.
(Note: A match held at Team A's venue is called Team A's home match and Team B's away match.)