All of our proofs and samples (orders for a single card) will have a barcode as they are intended as samples only.
These cards are meant to be a preview of the design to help make sure you've got the perfect one before placing a full order.
To receive a set of cards without the barcode, you'll want to increase the quantity from one to at least a pack of 20. You can do this by navigating to your Orders & Drafts page and selecting Order More.