401K IRA Contributions

I am over 50 years old and my wife is over 60 years old. I went back to work and will contribute 30000 to my work 401K.  Can I still contribute 8000 to my none working wife's IRA? 

Reading on the web says you can, then I hit a line that says you cannot if you have a 401K.  I do not understand what that means or if I can contribute to my wife's IRA. I thank you for any help that is given.