If the depth of the bed is only 6 or 7 inches, that will restrict what you can grow in terms of evergreen and deciduous shrubs - these would normally root down past the raised bed into the soil below.
Otherwise, it depends what you want to achieve really - 4 x 4 is a pretty small area and will easily be filled by a few plants. You might decide you'd like lots of colour in late spring up to fall/autumn, in which case, summer bedding would be good. Plants that will do well in this situation are Impatiens walleriana (and other Impatiens) tender Fuchsia, Begonia, Violas (Pansies) and Lobelia. These will all die or need replacing as winter arrives so if you can see the bed through a window, it's usual to remove them during early fall and replace with hardier things - new Violas, mini Cyclamen, ornamental cabbage, also known as flowering kale,though the latter two do prefer a little sun, along with small evergreen plants for contrast. In respect of evergreens, in the UK, small cuttings about 6-9 inches tall of various hardy shrubs are on sale specifically for temporary winter planting - I'm not sure if that's the case where you are.
For permanent planting, someone else has supplied a good list, but Geranium macrorrhizum also does well in shade, as does Liriope 'Munroe White'. Other cranesbill Geraniums may do well too, such as 'Wargrave's Pink', along with miniature daffodils such as 'Tete a Tete'. The trouble with these (as well as hostas and bleeding heart) is they all disappear in winter, though that may not be an issue if you can't see the bed through the windows anyway.