Start by computing the XOR coordinate values for all coordinates using a 2D prefix XOR approach. Initialize a 2D array `prefix` where `prefix[i][j]` represents the XOR of all elements from `(0, 0)` to `(i, j)`. Use the formula `prefix[i][j] = matrix[i][j] ^ prefix[i-1][j] ^ prefix[i][j-1] ^ prefix[i-1][j-1]` to fill this array.

Once the `prefix` array is computed, collect all unique XOR coordinate values into a list. Sort this list in descending order to easily access the `k`-th largest value. Return the element at index `k-1` from this sorted list.

To optimize space, avoid storing all XOR values explicitly. Instead, use a max-heap (or a min-heap with size `k`) to keep track of the top `k` largest XOR values as you compute them. This reduces the space complexity from O(m*n) to O(k) or O(m*n log k) depending on the heap implementation.