Andy Marshall and his side are in county finals action at the St Lawrence Ground in Canterbury, with Ashford their opening opponents in the last eight.
Overall victory would secure a regional play-off against the Sussex champions on February 14, followed by the regional finals a week later.
If they win that, the prize is a return to Lord's for the national finals on Sunday, March 14.
They've twice reached that stage, finishing runners-up on their last appearance at the Home of Cricket in 2007.