This is a question for you to answer for me, please
I am not sure why you need a grid type question to collect this information. Could you provide more information about exactly what information you are trying to collect?
In the United States, most state/federal government agencies and their contractors are supposed to follow OMB standards that mandate the use two separate questions to obtain race and ethnicity:
A radio-button question asking if the respondent is Hispanic or non-Hispanic.
A checkbox question asking for racial type(s) (American Indian, African-American, Asian, etc.).
Georgia Tech has a very clear explanation of this standard – http://www.ohr.gatech.edu/race%20definitions