Hi,
I don't see a problem there. You've restricted that shipping method based on the post code.
But on your frontend screenshot, you didn't yet enter the shipping address. So the system has no post code to use for the restriction and thus it doesn't display the shipping method. That's normal.
The shipping method should appear on the checkout once you provide the address.
Also, note that you apparently have the "include virtual products" setting turned off in your shipping method but you've selected a minimum amount. In that case, you need to have a weight configured in your products. Otherwise, the price of the products without a weight will be ignored for the "minimum amount" restriction. So that would be the total amount taken into account would be 0 and thus it wouldn't match the minimum amount restriction configured in your shipping method, causing it to not appear on the checkout.