First. Premiere is not the best tool to make a small size gif. Premiere is a video editor. You need a compositor.
Regarding a program, I use Hit Film which is free, and I also use Blender for 2D animation, (also free). If you want, you can use After Effects.
When using Blender you need to use emission as the shader.
Second. You need to plan your palette. This is probably the most important thing to reduce file size while maintaining a good quality.
The flat style is very good for an animated gif, and this is actually what revived the format. Use flat style and do not dither the image.
Export your animation-sequence as still PNG and assemble and export on another program, for example, Gimp.