Yes you can, and it had been done. The first time communism was associated with state atheism was with the USSR in Russia, but this was not the first time a communist system existed. New Harmony was a commune formed in Idaho and was made up of Christians, same could be said in the middle ages, where similar forms for government were proposed in books such as "Utopia" from which we get the term, this was written by a religious scholar, and suggested a society with no private property, and no government, instead people simply were good (and godly) and shared everything in common, using only what they needed. There was other suggestions for communist societies before then, dating as far back as ancient times, all of which were written by people who believed in the supernatural, specifically in religious concepts like God(s), afterlives, and the soul. Communism isn't an idea that's new, and it didn't start with Marx, its been around a long time, and the addition of atheism is only at the much later ends of the history of the ideology.