That is quite dismal! However, Aubretia likes full sun, so if that area is shaded most of the time, even if you could find a way to get some soil in it somewhere, it won't do well. I'd just paint it white instead, cheer it up a bit. You could try Campanula portenschlagiana or carpatica instead, but again, you'd need a pocket of soil for it to attach to. I assume the greenery protruding towards the top end is growing out of one of the drainage pipes...

I'm taking it that this is your side of the fence, so....
1. Paint the fence - lots of lovely colours available these days.
2. Paint the concrete 'wall' - painting it a light colour will make it stand out (useful as a reminder that it's there if you park cars near to it); a dark colour will make it recede.
3. Use troughs placed on the concrete wall with trailing plants and some taller plants, grasses etc to give variety.
4. Fix brackets (pot rings) to the fence posts and horizontal timbers for small pots of trailing plants.

A few other plants to consider besides aubrietia are lobelia, ivy, violas, spring bulbs, geraniums.... The list is almost endless.

Before you fix anything to the fence just double check whose fence it is. This is not the same as whose boundary it is. It may be a joint boundary (ie both properties responsible for its upkeep) but from the way the fence is constructed it looks as if you (or previous owners) actually installed the fence. If so you can drill into it without worry. If your neighbours paid for the fence then, out of courtesy, ask them if they mind you drilling holes in it BEFORE you set to with the drill!

Thank you both for your ideas. I will paint the wall and rest some troughs on it. Will send you a pic when I have finished my new project!

You could change the planting according to where the shade is - the far panel obviously gets the early morning sun. Does the rest of the fence get sun later in the day or is it shaded by the house?
Try an Internet search for plants for shady window boxes (or something like that) to get some planting ideas.

Don't forget that any troughs/pots will need watering in the warmer weather and add water retaining crystals to the compost to help.

Having go that far you could plant other things that would flower later in the year too.

The posts are on your side, therefore the fence is yours.

Just wondering how this fence transformation is going?