Is there any option to represent 160 discrete variables each one with their own color in scatter plot?
The number of colours you can use in a scatter plot will vary depending on what software or programming language you are using.

The main issue is that scatter plots might not be the best option to use if you want to distinguish 160 different variables, particularly if you are only distinguishing them by colour.

If you can group the variables you might be able to make it work with less colours, or consider using a different type of graph.