It depends on what the soiling is....engine grease or just light soiling?
I have the light grey too, and it has travelled with 3 kids under 12 for more than 2 years. It still looks pretty good...almost new in fact.
I followed the advice of an auto detailer....I use a solution of very dilute"de-greasing cleaner"...like 409 or Fantistic. I use the orange/citrus version. I guess I put about 1/8th cleaner in the bottle and the rest water.
I spray it lightly on soiled areas (including arm rests and center console), and then gently rub with a damp sponge. If it's stubborn, I may brush gently. I have a shop vac that I use to suck out the water afterwards.
Seems to work...although of course experiences will vary. My experience is that you don't have to go after it hard. Use very dilute cleaners and be very gentle.
Hope this helps.