This can immediately be answered: Manufacturing tolerances in any parameter like power supply rejection ratio, common mode rejection ratio, clock feedthrough suppression, phase margin, voltage noise, current noise, whatever you like. But this doesn't explain where the noise actually comes from. And it does not explain why it's sooo high!!

If there's relevant spike energy at input of OPamp (coming from LTC1064), then you should choose a bit faster OPamp than OPA4277. A slew rate of 0.8V/µsec can lead to dynamic distortion producing strange signal artefacts at output. Try a TL052A. That's a much faster chip often used for this purpose.

Do you have the possibility to make a spectrum of your observerd noise? Some scopes have a "spectrum analyzer" option. What is the result?

Again, please try everything I posted in my last reply. Especially the full disconnecting of analog circuitry from digital one. Connect a battery powered clock source directly to the clock inputs of LTC1064. This test will show, whether your application suffers from digital ground noise coupling.

Kai