1. An image processing device comprising: a print image data generator that generates print image data for each of colors to be used to print a document image from image data of the document image including a barcode image and a background image overlapped on the barcode image as a background; and a density adjuster that performs at least one of processing to reduce the density of the barcode image in at least any one of pieces of the print image data of colors including the barcode image and processing to reduce the density of the background image within a neighboring region that neighbors a bar of the barcode image in at least any one of pieces of the print image data of colors including the background image.