What is a piece of malicious code that has no productive purpose but can replicate itself and exist only to damage computer systems or create further vulnerabilities called?

Virus

A virus is a piece of software designed to infect a computer system. The virus may do nothing more than reside on the computer. A virus may also damage the data on your hard disk, destroy your operating system, and possibly spread to other systems. Reference: Mike Pastore and Emmett Dulaney, Security+ Study Guide, 2nd Edition, Alameda, Sybex, 2004, p 76