Maximum XOR of Subsequences

You are given an integer array nums of length n (non-negative values). Choose two subsequences (each can be empty and may overlap). Let X be the XOR of the first subsequence and Y be the XOR of the second subsequence. Return the maximum value of X XOR Y.
Note: The XOR of an empty subsequence is 0.

Key insight: The set of all subsequence XORs equals the set of all subset XORs, which forms a linear subspace over GF(2). Since 0 (empty subsequence) is allowed,

$$\max_{X,Y} (X \oplus Y) \;=\; \max_{Z\in\text{subset-XORs}} Z,$$

i.e., the answer is simply the maximum subset XOR. Compute it via a XOR-basis (Gaussian elimination over bits).