But if the current incumbents slip up Bury (68), who visit Northampton (66), Port Vale (67), who are at home to Shrewsbury, and Chesterfield (67), who face Bournemouth in the final match at their Saltergate home of the last 139 years, will be looking to pounce.
Grimsby, meanwhile, are second from bottom on 44 points, one point behind Barnet, but are currently in an excellent run of form having won four and drawn one of their last six games.
At the end of February the Mariners were seven points adrift of safety and 13 points behind the Bees.
But they travel to mid-table Burton knowing that only a victory at the Pirelli Stadium would secure their Football League status should Barnet lose or draw to already promoted Rochdale.
The Bees, who lost 2-0 to the Mariners last week, have lost six consecutive games, sacked manager Ian Hendon and appointed former boss Paul Fairclough until the end of the season.
However, the north London club have a superior goal difference than their relegation rivals.
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