Did you use GIMP to create that?
When I do .gifs in GIMP and change the color mode to "Indexed", I use the following settings in the "Indexed Color Conversion" box that opens:
*Generate Optimum Palette - Maximum number of colors: 255
*Color Dithering: Floyd-Steinberg (Reduced color bleeding)
*Enable Dithering of Transparency [make sure this box is checked]
This has produced the best results for me, so perhaps it'll help you, too.