It should be possible to have 8 14-2 teams in a conference, although it depends on the 2 floating games each team has. I don't know the specific details on those.
Scenario:
NFC always beats AFC, so each NFC team goes 4-0.
Top two teams in each NFC division go 5-1, splitting the games against each other.
Top two teams in each NFC division got 3-1 against the matched NFC division, losing their game to one of the top two opposite divisions teams. A1 > B1, B1 > A2, A2> B2, B2 > A1
That puts 8 teams at 12-2 with the two floating games left. If no floating game matched two of the 12-2 teams each of them could go 2-0. That's certainly possible if there are no interrelated restrictions on the floating games, namely no odd cycles, A vs B, B vs C, C vs A. I don't remember the scheduling rules well enough to say.