A running 4 stroke engine presents an extremely noisy (electrical noise) environment, mainly due to the ignition system firing. I would not be surprised to see some noise spikes with the oscilloscope sitting in the engine bay, especially with scope probes plugged in but not connected to anything or even without a probe/cable connected to a channel. An unconnected or incorrectly connected probe can act as an antenna and pick up noise. Even with nothing connected to the BNC jack, some noise will still couple in to the input. Ensure that you have the ground clip for each probe connected to a suitable location to minimise ground loops which will pick up magnetic fields. Locate the oscilloscope as far away from sources of noise (e.g. coil pack, ignition wires, battery cables) as is practical. Inevitably you will need to leverage the trigger functionality to reject any noise which remains to achieve a stable trigger (trigger hold off, HF noise rejection option, etc).
The only way to know if the scope is defective is to test it by a controlled measurement setup. Trying to measure signal off a running engine is clearly an uncontrolled setup unless you have another oscilloscope to compare.