Sometimes icons are stored in rather weird places. Searching for gantt in the Mint start menu search box should help you find it if it created a start menu item when you installed it.
Reading a little about Gantt Project online describes it as running in a Java virtual machine. Their project Handbook (which may be outdated) describes launching the program from a command line like this: java -jar ganttproject-VERSION.jar (substituting the correct version number for what you installed).
You may need to have your terminal open in the folder where the .jar file resides, or include that location in your $PATH.
