Need help - Match number in column, find lowest number in that row, and return header name

Hello, I am new here, been lurking and learning a lot. I have been able to figure a lot of things out from previous threads here but am asking for a little help with this please. Maybe there is a much easier way to do this but what I have so far is a sheet that contains a large number of zip codes in column A. I plan to have 6 or 7 zip codes across the top which each correspond to a store location. B2:H2000(ish) contain the number of miles between intersecting zip codes. What I would like to have happen is for the user to enter a zip code on a separate sheet and have the name of the nearest zip code be returned. I hoped I could figure this out on my own. I know this is probably not that difficult, I'm just not really all that bright. I hope this is a clear enough explanation of what i am trying to do here. Thanks in advance for any help.

Thank you for such a fast response. I am anxious to try it out, unfortunately I just left my office and didnt save it where it is accessible to me now. I think I was on the right track but it only worked when the lowest number was in the left most column. Like I said...im not that bright.

Thanks again, I think this is the last piece of the puzzle! Cant wait to try it out.

Okay, now I feel really dumb. I'm sorry to have to ask again for help. Stumped again. That formula worked perfectly, thank you again. Now what I am wanting to do is return the lowest number in the row with the matching zip code. I know I should be able to figure this out, sorry and thanks for any help.

Thanks again, I think I'm done now. I appreciate your help very much, I'm starting to think I'm never going to get this. My brain might just not work this way. I guess it would help if I knew what i was doing.

Thanks again!