The ADC needs a very, very stable voltage reference. Any jitter on the reference or ground, and you will quickly loose one or more of the bits.

Whatever you do, you just must make sure that you don't have any jitter on your voltage reference or ground.

Next thing is that just measuringa absolute values means that the tolerance of the voltage reference will affect you. So you either need a voltage reference way better than 0.1%, or you need to cancel the errors of the voltage reference. This can be done by making two measurements - one with unknown resistor and one with a known resistor and use the relation between the two instead of the absolute value.

Which method have you selected. Trying to have a very stable voltage reference in a temperature-controlled owen? Or trying to measure the relation between a known resistor and an unknown resistor? In the second case - how do you try to do this?