If it's in shade a lot grass probably won't do too well.
I suggest you look up RHS (Royal Horticultural Society) or BBC Gardeners World sites and see what they suggest for small shady gardens
There are plenty of plants/shrubs suitable for shade or semi-shade. Bulbs are easy; we have hundreds of snowdrops at moment, and they can be divided every couple of years; may self-seed if they feel happy! Crocus in many shades, daffs and narcissus, small ones if small garden. Hellebores quite easy and can be very colourful in a subdued way, also heuchera, and pulmonaria (lungwort - hairy leaves can irritate skin) are all happy in shade. Cyclamen are pretty, the small 'wild' sort and I think there are spring, autumn and winter flowering varieties. Don't bury them, just plant ON SURFACE of soil; corms may be expensive, but spread easily. After flowering they make seed capsules (like small Maltesers) which open when ripe, and the sticky little seeds can be scattered around and you'll have hundreds in a few years! Hostas as versatile, but slugs LOVE them!
(I am not recommending the following sites, but they are just a selection that came up to show what the flowers look like. The Sarah Raven cyclamen is Indoor, but she has an interesting site and knows her stuff!)