Sorry I clicked like by mistake. Try the manufacturer of the rod you have for a suitable case. I have cases from Shakespeare, Tricast, Drennan, Middy and Preston and they suit 13’ rods perfectly. Middy make a padded case for 11’ 2 piece rods so will fit a 13’. They are called Middy Xtreme series( about £20) are good value with quality zips.
You have to be careful buying these cases mail order. I sent off for a Greys Prodigy 12' case. It's very well made, a quality item. But my 12' 2 piece rod sticks out of the top unless you push it down hard and really stretch the zip up - and who wants to do that over the tip of your rod? I couldn't see why the dimensions were cut so mean - like those shirts spoiled by making the sleeves an inch too short. On another occasion. I'd take the rod to the shop and try it.