The final relegation spot is between the Bluebirds and Woking and although the 0-0 draw at Bromley on Tuesday night changed little, safety remains very much in their hands.
The Cards must beat Dover Athletic or it is they who will fall from the Vanarama National League.
If Barrow beat already down Chester then it doesn’t matter what Jason Goodliffe’s team do against a side chasing the play-offs.
Things are certainly in Barrow’s favour but Pennock wouldn’t hear that they are almost safe.
“There’s still a massive job to do,” said the former Gillingham and Forest Green Rovers manager. “We have a big day in front of us.
“We have to just focus on ourselves but this was a pleasing point. To come away from Aldershot and Bromley without defeat is a real positive.
“We had to ride our luck at times. It was a bit heart-in-mouth but we deserve the slice of good fortune after Aldershot scored against us in the fifth minute of injury time on Saturday.
“Now it’s full focus on Chester and keeping the club up,” he added.
“We’ll be ready and I just hope that the whole town turns out and that the ground is bouncing because the players need that support more than ever.”