At the suggestion of Wolf, DK4RW, I have added a low pass filter into the low power audion stages of the GQ-20. The filter removes most of the fairly high hiss level from the MC1350 chip, which otherwise tends to mask the desired signal. The mod will be useful on other rigs as well, and so you might like to see the original details from Wolf:
In order to improve the sensitivity of your GQ-20 you might consider adding an AF low pass filter between R20 and C40. In my GQ-40 I used a two stage elliptical filter :
A 0.2uV RF signal yields a S/S+N ratio of 3.5 dB in my unmodified GQ-40. With the filter and the same RF signal the signal to noise ratio improved to 10.5 dB. This improvement might not look very impressive but it makes a _significant_ audible difference. The filter removes nearly all the high frequency hiss which I felt rather annoying in the original version.
Not only does it reduce the unwanted noise in the GQ-20, but (I believe) makes the recovered audio nicer to listen to. Thanks to Wolf for this useful idea.