Thank you @György-Farkas for detailed answer.
I've tried this ADC (on demo board) on Arduino and also received nothing.
I think that this board is broken.
I bought ADS1115 and now I can smoothly read from photodiode :)
If somebody will need that in future guys from Control Everything Community made working python example for Omega2.
(or at least it's working in my case with FW: 0.2.0 b191)
@yaseen-almanna From reading the data sheet for the MAX11665, it looks like it should be possible to access it using SPI. While I am not highly familiar with SPI usage on the Omega, doing a quick search shows that there are available opkg packages. It may be worth looking at the following packages:
Additionally, for ADC, it may be worth looking at I2C based ADCs. I have successfully used the following that uses I2C connected to my Omega: https://www.adafruit.com/product/1083
Though I don't actually use it myself, there is an opkg package for this: