Danny McSheffrey's side won their first game in the competition in four attempts with a 2-0 victory over Banbury United last Tuesday and have been drawn away to Conference side Solihull Moors who put Coventry City out of the competition in 2008.
The date for the game is to be announced.
The full draw is as follows:
Rugby V Highgate, Stratford V Nuneaton, Stourbridge V West Brom, Sutton Coldfield V Tipton/Walsall, Coleshill V Birmingham, Boldmere/Hednesford V Bedworth, Alvechurch/Chasetown v Rushall/Redditch.