I hand washed mine, as felt a washing machine cycle could beat them up too much and weaken glued and coated areas.
My 22yds looked just like that, maybe a tad worse and got them looking about 85% better. I stripped off the laces and machine washed those in a whites wash, then got a bowl of hot water and a nail scrubbing brush. Take out the inner soles and submerge into bowl of hot water to wet the shoe, spritz on some Vanish stain remover spray and agitate dirty areas with the nail brush, rinse and then repeat as necessary. Some areas will require working from inside the shoe, where dirt has got behind the plasticised external coating.
I then prop the shoes up vertically with the heels on the ground, to try drain water out the fabric within the toe box area. After about half a day I then squeeze out the last bits of water from the heel. Finally pop them into a warm area, ideally like an airing cupboard but a radiator with hand towel underneath would be ok. You don't want a fierce heat to dry them out too quickly.
Next time I might soak the shoes overnight in a bowl of water and powdered stain remover, like I do my cricket whites to try improve on the results.