If you check carefully, the noise is mostly 2 LSB with some 3 LSB peaks.
So, if the ADC range is 0-255 and we have a "127" input signal, the noise would be doing 127,128,126,127,128,129,126...
I wouldn't expect anything better from a cheap scope running 1GSps ADC in a 2-layer pcb.
Perhabs wrapping the whole board in copper foil and grouding it would help.