I'd avoid using anything containing live grass for fear that the grass might sprout and become a problem. (Grass has a way of growing even when sod is turned upside down.) If you can handle the wait, kill grass by putting layers of newspaper over it, topped by shredded leaves, yard waste, well-rotted manure, topsoil, peat moss, and grass clippings. After a few months, turn this temporary compost pile to create a fine raised bed. Alternatively, you can make raised beds from good, loamy topsoil, or mix compost with your existing soil to build up the raised bed.