I finally cleared the level. The key is to try and clear red, blue or brown squares on every turn. I focused on the colors and tried to swap with the brown squares so that I could clear them without moving the brown squares too much. I also moved out the center dot cluster immediately and tried to use the platform as much as possible to clear the colors. This enabled me to clear at almost every turn. I did have to use one continue to finish off my last 3 dots. So save your continues - this is the level to use them.