pattern - Really, really, really hard sequence

... in which you have nothing to do with math
... except maybe with some counting and this and that
... but no calculations, no, definitely no.

$1, 0, 8, 62, 90, 68, 83, 89, 88, 057, 619, 028, 693, 069, 068, 985, 086, 988, 871, 820, 838, 865, 890, 868, 887, ?, ?, ?, ...$

Question:

What are the next elements?

Hint 1:

4 is missing for reasons.

Hint 2:

4 is too much.

Hint 3:

4 is somehow ambiguous.

Answer

The next numbers are:

$889, 888, 0123$

Because

they are ternary representations of the natural numbers starting at $0$, where the trits are the number of holes in the base $10$ digits
The next ternary numbers to represent are $221, 222, 1000$.
You are cycling through $(0,6,9)$ for those with one hole,
through $(1,2,3,5,7)$ for those with no holes,
with just $8$ for two holes.

$4$ has a hole so it could be used but you decided not to do so because it may also be written without one
($0$ could be written with a slash through it too, giving it two holes).