There can be several reasons for this. If the barcode looks fuzzy on screen, please remember that most computer screens have a resolution of either 72 or 96 DPI. What matters is how the barcode will print out. DPI is a property of the printer and the printer's software and not the graphic design program you are using.
Not knowing how to work your graphics application properly is the biggest reason why designers and self-publishers struggle with their barcode files, and frequently have problems with barcodes looking blurry or having lines crossing through them. Unfortunately, there's not just one reason for this.
In some software applications, when a barcode file is imported, the dpi is automatically changed to the screen dpi (72 dpi) instead of maintaining the original dpi of the file (ex., 300 dpi or higher). You will need to reset the dpi of the barcode file.
When you import an eps file into Photoshop, the file is changed, the dpi is lost, the size is lost, and the image opens on a transparent background (you need to place it on a white background), among other problems.
Other potential problems include "anti-aliasing" during the conversion of the encapsulated postscript to an image and the "jpeg" compression that will generally occur in PDF creation. These can damage your barcode and make it scan with errors when printed. Jagged steps on the numbers of the barcode are due to the lack of "anti-aliasing," a technique for using shades of gray on slants and curves to make the edges seem more smooth to the eye. Do not use grayscale. Import as black and white. Importing as black and white might in fact be better for some applications.
Many applications do not provide an accurate preview of barcode graphics. Instead determine the quality of the image ONLY by the actual printout of your barcode. Never judge your barcode from the onscreen preview.