I've created my Google Custom Search Engine here https://www.google.com/cse
When I add it to omnibox with rightclick and try to use it I receive:

It's not unexpectable because search url in that case is:
https://www.google.com/cse/publicurl?search=%s&bgresponse=
while my public url looks like that:
https://www.google.com/cse/publicurl?cx=239428934982349832894:slkdfj9024
So, how can I add Google Custom Search to omnibox or is such possibility totally blocked by Google intentionally?