Qt::Tool windows cannot be made Qt::WindowMinimized

I'm trying to implement a Window menu that provides some standard menu items like Minimize and Zoom.  If a window is not minimized, my code tries to minimize it by doing:

activeWindow->setWindowState(activeWindow->windowState() | Qt::WindowMinimized);

I'm surprised to discover that, for some windows in my app, this results in a console log that says "Qt::Tool windows cannot be made Qt::WindowMinimized".  This is strange, because these same windows have a minimize button in their title bar, and clicking that button does indeed minimize them to my macOS Dock.  I just want to reproduce the same behavior with a menu item with a command-M shortcut, as is standard on macOS.  Why does setWindowState() refuse to do it, given that it is otherwise possible?  Is there a workaround?