Try some mechanics hand soap... specifically the one that has pumice in
it. Most hardware stores sell it in a gallon pump jug.
The best one to get has natural orange in it. It smells like fresh
oranges and its gritty and creamy. All you do is poor it on thick and
scrub, and then rinse off afterwards with a garden hose. It's also
environmentally safe.

I swear it will take the dirt or grease off damn near anything. Just
to give you an idea of it's power...I had a white shower stall floor
with stains that would not come out with any household product that my
wife tried...including bleach, etc...So as a last ditch effort, I tried
the mechanics soap with a small brush and scrubbed.
It worked, the shower stall looked like brand new when done.

I think it has 1000 possible uses as a cleaner...good luck.