If your hands look like you've been working in a coal mine after a single belay session, it's time to give your cord a bath with some Beal Rope Cleaner. This rope-friendly detergent won't damage polyamide fibers nor will it leave a residue on the sheath.
Keep your ropes strong. Beal's Rope Cleaner is anon-aggressive detergent developed to clean ropes and Harnesses easily. It comes in a 1 L bottle.
Non-aggressive detergent developed to clean ropes and Harnesses easily. Will not damage polyamide – water temperature < 30°C.
If you are paranoid about throwing your line in with standard laundry detergent, this is a good option and does indeed get your rope cleaner than washing with water alone. There are lots of resources out on the web detailing how to wash a rope but this one is to most succinct and correct in my view, as it includes instructions for a frontloader, toploader or bathtub washing method: