It's not that different to mine, which was a 10m x 10m sqaure of grass, with a couple of small patios when I moved in. Newish build (yours looks like it might be).
You can absolutely build a garden into that. Some of the things we did:
- Worked out where we'd like to sit first
- Then worked out the 'eye lines' for how that space could be overlooked
- Planted strategic trees in the eye line to break up the line of sight
Once we'd done that, I dug a border in round the edge that is wavy - it kind of curves inwards each time it gets to a tree so the tree is included in the border.
That left an awkard square next to the shed, where I built a small pond - this has been the single thing to make the biggest difference about wildlife.
I then watched where the sun as so figured out which bits get the most sun and planted accordingly. Many things thrived, some failed - when they failed I replaced them again with something else.
The other thing I did has been to feed, feed, feed the soil and lawn. New builds tend to have crappy soil but mine is lovely stuff, mainly because I build the borders up with a 10cm layer of top soil and each winter I mulch heavily with manure. I feed the lawn but also do all my repotting on it - so there is plenty of compost overspill that helps deepen and feed the soil bed there. Also, the dog pees on it, so that helps 
We don't weed the lawn, so long as it's green that's good enough for me.