Hook up your probe to a Jim Williams pulse generator (see https://www.eevblog.com/forum/blog/eevblog-306-jim-williams-pulse-generator/) and see what the ringing looks like. If its period is similar to that you are observing in your oscillator circuit, odds are, its a probe artefact.
Now where do I get that kind of pulse generator in a short notice?
Build it Manhatten style on a scrap of copper clad FR4 - the 90V supply can be done with 10x really cheap zinc carbon PP3 batteries from the market, so you can discard the PSU circuit (the 10Meg-24K divider chain + everything to the left of it). For the 50R emitter resistor, its best to use two 100R SMD resistors upside down either side of the output pad to minimise inductance. Breadboard the circuit with 100pF for C2 and if you cant easily source a few 2N2369 transistors to try, try different low Vceo, high Ft transistors till you find one that pulses reliably. RF transistors are more likely to avalanche than most switching transistors. If you are using a through hole transistor, its probably best to drill a hole in the PCB and mount it up-side down for minimum lead length. Caution: metal can transistors usually have the can connected to the collector - you'll need to countersink the hole slightly to remove a ring of copper to avoid shorting it out.
See AN47, appendix D, page 93 of
http://www.linear.com/docs/4138Also note that C2 can be replaced by a long length of coax for a flat(ish) topped pulse. 10m of 66% velocity factor coax will give you a pulse duration of about 50ns, which will resemble a half cycle of a 10MHz squarewave.