Yes, you can grow raspberries in raised beds.  It is good to till the ground first to give the roots a direction to grow towards when you add the bed on top.  It is also helpful to mulch the raised bed.  This helps retain moisture, reduces weeds and helps insulate the roots until snow covers the beds and provides additional insulation.  Two feet above ground level is a good depth for the reasons explained in the following websites.  You could do less height; just be sure the beds are not too narrow and can’t properly insulate the plants during winter.

1. https://extension.umn.edu/fruit/growing-raspberries-home-garden  
2. https://extension.umn.edu/yard-and-garden-news/planting-and-trellising-raspberries
3.  https://www.epicgardening.com/raspberry-raised-bed/