I don't have any way for optimizing a home/away schedule like this, so all I could think of was to modify an existing schedule. I started with Warren's schedule for 14 players that you can
generate here and then moved some of the matches from the first 6 rounds to create the last round. It will probably not keep the byes as far apart as you would like.
1: 13-2 12-3 11-4 10-5 9-6
2: 7-9 5-11 4-12 3-13 2-1
3: 1-3 12-5 11-6 10-7 9-8
4: 8-10 7-11 6-12 5-13 4-1
5: 2-4 13-6 12-7 11-8 10-9
6: 8-12 7-13 6-1 5-2 4-3
7: 3-5 2-6 1-7 13-8 12-9 11-10
8: 10-12 9-13 8-1 7-2 6-3 5-4
9: 4-6 3-7 2-8 1-9 13-10 12-11
10: 11-13 10-1 9-2 8-3 7-4 6-5
11: 5-7 4-8 3-9 2-10 1-11 13-12
12: 12-1 11-2 10-3 9-4 8-5 7-6
13: 6-8 5-9 4-10 3-11 2-12 1-13
14: 8-7 6-10 13-4 3-2 1-5 9-11
take the team on the left to be the home team, and the one on the right to be the away team.