Doing that and being consistent with the rest of MATLAB would require that you write a new MATLAB Object class with its own subsref() and subsasgn() methods, and possibly reshape() as well. You are asking that data be stored in a different order than MATLAB normally stores it. All kinds of routines (such as sum() and mean()) expect data to be stored in the MATLAB order.
However, it is possible that for your intended use, you just need to know how to re-order a vector with (36 * 36) elements so that it fills memory in to a 4D array with your desired order. If so, that can be done with transpose() and flipud() and fliplr() and permute() and reshape() in combination. You might not need all of those in practice for this particular order. (I haven't yet worked out a good reordering sequence for this.)
