Maximum stud centre's are 600mm and common studs are 35mm, that gives you 565mm between the studs. There's a very good chance there will be a load bearing stud you will have to cut out which I would highly recommend not doing. It's a little hard to say what your options may be without seeing what you are up against, can you post some photo's? Does this wall have a window/door near the dishwasher opening? also is the roof a truss roof? It may have a girder truss loading on it? As much info on the frame as you can, some photo's of the inside of the roof above the dishwasher would be helpful.