dsPIC33FJ128GP802 audio DAC very noisy

The initial post:
 
I want to get started into real time audio processing and decided to begin with using the
dsPIC33FJ128GP802 because it has a 12 bit ADC, DSP engine and 16 bit audio DAC.
I have implemented a PCB - see here: https://www.dropbox.com/referrer_cleansing_redirect?hmac=1N2jIo9tYYtXJ2tl7D%2BGIEW36V2NtC7IolaIq6hkuE4%3D&url=https%3A%2F%2Fwww.dropbox.com%2Fs%2Fd9jl4lgph15uvl5%2F180326%2520PCB%2520plano%2520foro.pdf%3Fdl%3D0 .
 
Everything is working fine, audio is coming out with good quality, except I am having a great amount of noise in the output (I have no instrumentation in order to measure the amount of noise and quantify it, sorry). I have made many tests and everything indicates that the noise is being generated in the DAC module. Here are some tests I have made:

Set the DAC output register to a constant value. There is no audio going out, but the noise remains exactly the same.Turn off the DAC module. Noise disappears.Connect things as in https://www.dropbox.com/referrer_cleansing_redirect?hmac=TVbGFxRxPl20aJW8YDcvAPuAd19swMjJsYl3UcPsT%2Bc%3D&url=https%3A%2F%2Fwww.dropbox.com%2Fs%2F5zvhiura5lfr3ck%2F180326%2520PCB%2520plano%2520foro%25202.pdf%3Fdl%3D0(while keeping DAC module on), I get good audio quality and noise disappears.

Searching with Google I have found that some people had the same problem in the past (see https://www.microchip.com/forums/m479331.aspx for example).

What do you see on a scope?
One thing I have noticed about these DACs is that there is a 'default' value. If you do not keep the input buffer with at least 1 value available, then the default value will be inserted into the stream. The effect of this can be to introduce noise into the output.
I prefer to use the LITYPE/RITYPE bits to 0 which causes an interrupt if the FIFO is not full.
Susan

Now that I can post (after months awaiting for the moderators approval) I confirm that my problem was effectively generated by the 60 dB of SNR specified. I am not a digital audio expert, this was my first experience. I thought that 60 dB would be enough. After all it's an audio DAC, intended to be used with audio... In my experience, the 12 bit ADC has a much better performance for audio applications than the 16 bit "audio" DAC. Maybe this is obvious, it was not for me at a first glance. My conclusion is that this "audio" DAC is not really useful for audio applications.