##JavaScript, 27 numbers

Very similar to [TuukkaX's answer][1], with another set of digits.

 5789%

The 27 distinct values are:

 589 % 7 -> 1
 987 % 5 -> 2
 978 % 5 -> 3
 879 % 5 -> 4
 985 % 7 -> 5
 958 % 7 -> 6
 975 % 8 -> 7
 95 % 87 -> 8
 9 % 875 -> 9
 97 % 85 -> 12
 89 % 75 -> 14
 95 % 78 -> 17
 78 % 59 -> 19
 79 % 58 -> 21
 98 % 75 -> 23
 87 % 59 -> 28
 89 % 57 -> 32
 97 % 58 -> 39
 98 % 57 -> 41
 57 % 98 -> 57
 58 % 97 -> 58
 59 % 87 -> 59
 75 % 98 -> 75
 78 % 95 -> 78
 79 % 85 -> 79
 85 % 97 -> 85
 87 % 95 -> 87


 [1]: https://codegolf.stackexchange.com/a/102664/58563