Banning free speech is unconstitutional. Any "Code of Conduct" or other self proclaiming binding clauses on your contract that try to go against your constitutional rights should be void.
Banning free speech is absolutely not unconstitutional. I think the Wikipedia article[0] sums it up best (emphasis mine): In the United States, freedom of speech and expression is strongly protected from government restrictions by the First Amendment to the United States Constitution, many state constitutions, and state and federal laws.
