Is this ADC capable of better performance?
In the comments you stated that the problem is noise in the circuit. That is a crucial bit of information that you left out of your original question. If the problem is circuit noise then changing the ADC range isn't going to help.

First, you need to understand the noise. Take an FFT of the noise and see if it has a large component at your local power grid frequency. If so, then you clearly need to clean up your power supplies. You should also try running the whole thing from batteries using only linear regulators to see if that helps.

Make sure that the noise isn't coming from the digital side of your design. The AVDD and DVDD lines should be well isolated. If these two supplies are tied together at some point you may need to add passive LC filtering between them. You haven't told us how you physically constructed the circuit, but the proper routing of power and ground on a PCB is also important.

If the noise is truly random with a Gaussian distribution and its amplitude is greater than 1/2 LSB then you can use oversampling to improve the effective resolution of the measurements. In this case, averaging four measurements will improve the resolution by 1 bit.