Assuming you are only using vectors (pen tool, shape tool, etc.) in Illustrator to create your image, your artboard can be any size that's proportional to the dimensions of the final banner. This is because vector graphics can be scaled to any dimensions and retain sharp edges.
If you are using any raster (pixel-based) images, such as a JPEG photograph or something that has gone through Photoshop, you will need to create the artboard at 108 feet long and set your raster image at 300 dpi at the actual printed size in order to ensure that element will print at high resolution.
If you are using any raster (pixel-based) images, such as a JPEG photograph or something that has gone through Photoshop, you will need to create the artboard at 108 feet long and set your raster image at 300 dpi at the actual printed size in order to ensure that element will print at high resolution.