Hi Jesse- welcome to the forum- Stop by the intro page and say howdy.
My cross references do not show a Model 40. That may not mean a lot- there were a LOT of companies that made guns marked with the Sears JC Higgins brand. One that was close to yours is the JC Higiins Model 45- which is a Marlin 336 carbine. That is the second most popular deer rifle in the US.
Pictures would help, along with ALL of the markings on the rifle.