What program are you using to create the heightmap? I have two art programs installed on my laptop, Paint.NET and GIMP 2. Images made with Paint.NET always crash my FH upon an attempt to load them in the map maker, but images made with GIMP can work.
This is because even if the entire thing is filled in perfect grey, FH never recognises maps made with Paint.NET as a grayscale image. GIMP, however, has an option where you can switch to the computer recognising it as a greyscale image. Once I export it after using that setting, FH doesn't crash upon loading the height map. It's a bit weird, I know, but that's how it works.
Don't worry, you don't need to entirely re-make the height map. You can also just open the image file in GIMP, turn the setting to let FH recognise it as gretscale image, and then export it as either a .png or a .jpg file. Unfortunately, I can't see from here what art program you're using or whether your art program has this option. If your art program doesn't have the option to let your PC recognise it as a greyscale image, you'll unfortunately have to download GIMP or an other art program that does have that.
I hope it helps!