https://www.scirra.com/blog/112/remembe ... our-memory
Rather than enlarging your game resolution, you may want to consider reducing the resolution of your image with an editor.
Generally speaking, you won't be able to use a large map all as one huge sprite. As described in the linked blog post, game developers will usually use a mixture of techniques to manage memory: tilemaps, repeating backgrounds, smart placement of transformed detail sprites, and the occasional big budget centerpiece.