Yes, they can
You already outline all the calcuations.
Long Jump from running start is Strength feet (24), d20 adds 20 to the Strength (Athlethics) check ability check on a natural 20, proficiency at level 20 adds +6 and the Strength bonus adds +7, for a total of 57.
However, jumping counts against movement (except when you are a harengon with a special jump action), page 182 PHB, Jumping:
Long Jump. When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump. When you make a standing long jump, you can leap only half that distance. Either way, each foot you clear on the jump costs a foot of movement.
So to realize this they would need to have a speed of equal or greater than 10+57, for example from haste, which grants double speed. Or you could use the Dash action, which also increases your movement for the turn. Otherwise your jump would be limited to your normal movement speed, wich for a Barbarian starting with 30 feet, at level 20 would be 40 feet (if not wearing armor, due to the extra 10 feet from the level 5 feature Fast Movement), or 30 feet after the 10 foot running start. As a tabaxi Barbarian, you could use your Feline Agiliy to double your normal speed and achieve the full jump without external help or dashing.