If you have a rooted Nexus 4 phone, it is easy to safely get better both audio and video output quality with the camera. Just improve it by changing the camcorder bitrates. Here is a tutorial about how to do that.
* First backup your device data. If the method fail, you caould restore without any damage.
* Download and install ES File Explorer from store. Within the app, mount the System as Read-Write mode and go to /system/etc folder.
* Find out the media_profiles.xml file and use Jota Text Editor to access it. Locate the code "<EncoderProfile quality="1080p" fileFormat="mp4" duration="30">", change the Video bitRate from "12000000" to "20000000" and also Audio bitRate from "96000" to "288000" respectively. Once finished, save the setting and restart N4, and then you are able to enjoy recording 20Mbps video with 284kbps sound captured.