You should always "dig in" any giant vegetable deep with lots of organic matter, take extra care over feeding, watering and pest control and, if showing, harvest at the very last moment for freshness.
Fill a 6in-wide 4 foot long drainpipe with clean fine sand. (Always be optimistic). Make a hole in the sand with a long pole and fill it with good potting compost. Sow three seeds in the compost and thin to the best one when they have germinated.
Water from the top for the first two months and thereafter from the bottom to encourage the roots to seek out moisture. At harvest time wash out as much sand as possible using a hosepipe before very gently pulling up the carrot. If you pull too hard you may damage the long tapering root. The longest carrot was grown by Bernard Lavery. 16 feet 10 1/2 inches. You can still purchase his book on Amazon "How To Grow Giant Vegetables" Good luck.