The Matlab Desktop is not available in compiled application, and for a very good reason - otherwise users could compile and distribute a free program that mimics Matlab. Therefore, you cannot compile something that looks like the Matlab Desktop, with integrated console and figures in the same window. There is a technical way to dock figures in deployed programs, but it will be to a separate figures window, which is separate from the console.
I suggest that you modify your program so that all user interaction is done in a single (non-docked) figure window that has 2 panels: one panel displays the graphics results of your program; the other panel accepts user input text and interaction. This unified figure GUI can then easily be compiled and will work the same way when you deploy it as a standalone executable.
