In the case of linear codes, this is the same as asking for non-equivalent codes with the same weight enumerator.  There are many examples known.  Search for "same weight enumerator" at google scholar and you'll find some examples quickly.

For example, [this paper][1] and [this one][2] and [this one][3] and [this one][4].


  [1]: http://www.springerlink.com/content/hj40064667223702/
  [2]: http://www.win.tue.nl/~ruudp/paper/57.pdf
  [3]: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=748461&url=http%253A%252F%252Fieeexplore.ieee.org%252Fxpls%252Fabs_all.jsp%253Farnumber%253D748461
  [4]: http://arxiv.org/pdf/math.CO/9310227