Hello Florijan,
The gain available from the PGA would seem to be unsufficient - the output from the PGA will increase the analog level to about 1.7 percent of full scale. This would produce a maximum count of 71, giving an effective ADC resolution of about 6 bits. The inclusion of an external low noise preamplifier, with a gain of 50, would improve the results.
The effectiveness of your averaging process will be influenced by the number and timing of the individual readings. If some of the fluctuation is due to the presence 50 Hz mains hum components, the readings should be taken over a 20 millisecond period, or a multiple, to average out the hum.
Regards,
Mac