Never heard it called Gibbs ringing before but I assume you're observing overshoot and then some oscillation prior to stabilizing.
High-frequency oscillations are quite a common source of overshoot and ringing due to their fast edge rates. It is worse when the crystal is far from the ADC (and by "far" I mean anything >20mm or so) or the traces between crystal and part are not as short as possible.
A little bit of ringing is OK, but more than about 10% of steady-state is a potential source of concern, not in terms of damage but just in terms of a "misbehaving circuit".
The Flexible MIDI Shield
: MIDI IN/OUT, stacking headers, your choice of I/O pins