X is 10,000-by-60 Y is 10,000-by-60
X' is 60-by-10,000 Y' is 60-by-10,000
By correlating these two matrices, i.e. R=corr(X', Y'), you get the 10,000-by-10,000 R matrix whose elements are the pairwise correlation of each column of X' and Y', that is each row of X and Y.
So, you are doing the right thing! Just check the diagonals of that matrix:
>> Rvec= diag (R)