This is a twenty gallon, which are relatively good for ball pythons. HOWEVER, what you are describing is a 20 gal Tall. You want either a 20 gal long or a 20 gal wide (breeder) The tall tanks provide less floorspace and make controlling temperature more difficult. While ball pythons do like to climb, they will spend the majority of their time on the ground.
A ten gallon is ideal for a baby. The tank you have now would be too big. Too much space freaks out this species. I suppose if you added many different hiding places in the tank and cut down on open space it may be okay. Can't guarantee that though.
Really, I do not recommend the tall tanks--especially if this is your first snake. Ball pythons are notorious for refusing to eat, developing health problems, etc, if temperatures or humidity are even off by the slightest bit. The tall tanks make temperature harder to control.
A 20 long or wide would be suitable for an adult ball python between 3-4 ft. If you get the 4 1/2-5 footers, you may want to consider upgrading to a 30 or 40 gallon. The minimum amount of space you want is the area of the tank (length x width) should be at least 2/3 the length of the snake.
Feel free to send me a message if you have any questions about what I said above.