Preheat the oven to 180°C.
Score the inside of the squid body, cut into pieces, and set aside.
Heat the olive oil in a paella pan and fry the onions, garlic, and sliced chorizo.
Add the drained pearl barley and stir for 4 minutes to coat in oil.
Stir in the saffron and its soaking water.
Add the peppers, tomatoes, artichokes, and paprika and stir until combined.
Pour in the warm stock and bring the mixture to a boil.
Arrange the grey mullet, squid, prawns, and mussels on top.
Cover tightly with foil and bake for 25 minutes until the barley is tender.
Serve the paella garnished with lemon wedges.