$ 15 $ teams participate in a soccer league. Each team plays each of the remaining teams exactly once. If a team beats another team in a match they receive $ 3 $ points, while the loser receives $ 1 $ point. In the event of a tie, both teams receive $ 2 $ points. When all possible league matches are held, the following can be observed: $\bullet$ No two teams have finished with the same amount of points. $\bullet$ Each team finished the league with at least $ 21 $ points. Let $W$ be the team that finished the league with the highest score. Determine how many points $W$ scored and show that there were at least four ties in the league.