Where do you put the filter and the load?
The oscillator may experience problems when driving a filter and or a 50 Ohms load. When it remains oscillating, you may expect some 200mV output voltage.
Weird things may/will happen when you directly connect an LC filter to the collector (don't forget DC decoupling capacitor). Virtually all filters show wild impedance behavior outside the pass band. This will affect the phase shift and gain of the BJT amplifier. The oscillator may oscillate at another frequency and/or with unstabie amplitude.
I would first try to understand how the circuit operates (so you can make good educated guesses) and then play with the design so that you have a reasonable sinusoidal wave shape. It will not be easy as the loaded Q factor for the LC circuit is relatively low. When done, use a second stage (buffer) that provides some isolation between the oscillator and the load+filter.
As a buffer stage, you may use a common collector stage (emitter follower) where you put a 50 Ohm resistor between the emitter and the actual output. Both the input and the output of the filter (that you have to design) "sees" about 50 Ohms. You may know that if you have a single transistor emitter follower running at 10 mA in class A, you can only get about 400mVp into 50 Ohms.
If you need several volts of output into 50 Ohms. you may use a complementary class B output stage (with PNP and NPN transistor).