I have just taken a very quick look at this, so I can't swear this to be gospel as it's not a thorough analysis, but I think that it pretty much represents the position:
From the start of the 2012-3 season up to now, for all league teams that were not in the Premier League during that that time (because they would have played less games during that time, thus distorting the results), the teams with the least draws are listed below:
Peterborough 19
Stevenage 23
Leeds 27
Crewe 27
Rochdale 27
Orient 27
5 teams 28
4 teams 29
Bees + 8 other teams 30
If we include the 2011-12 season, Peterborough still seem to come out on top with 30, followed by Swindon on 35 and Port Vale on 37. The Bees are some way behind on 43.
Not so, I'm afraid. From the start of the 2011-12 season, Peterborough win again with 10, followed by Port Vale and Notts Co. on 13 , then Bees, Rochdale + Stevenage on 14.
HTH