Sorry it needs. 365 gain.
It is simple to cascade two transistors to make a gain of 365 and have an output swing of of 8V and an output of 10k ohms. Here is a simple design found in Google. If the first transistor has a gain of 40 and the second transistor has a gain of 9.125 then the distortion will be reduced.
Of course the high gain transistor (2.4V output/10mV input= gain of 240) has distortion, the output is high level and there is no negative feedback.AG, that circuit has some serious distortion! - can't you see how asymmetric the output is?