Is the Couvreur et al. polynomial time attack on McEliece practical? There's a new e-print out on arXiv titled "A Polynomial Time Attack against Algebraic Geometry Code Based Public Key Cryptosystems" by Alain Couvreur, Irene Márquez-Corbella and Ruud Pellikaan:


  "We give a polynomial time attack on the McEliece public key cryptosystem based on algebraic geometry codes. Roughly speaking, this attacks runs in $O(n^4)$ operations in $\mathbb F_q$, where $n$ denotes the code length. Compared to previous attacks, allows to recover a decoding algorithm for the public key even for codes from high genus curves."


Is this a practical attack against currently used implementations of the McEliece cryptosystem, with security parameters such as those recommended by Bernstein, Lange and Peters (2008)?

If the answer is yes, then how much do we need to increase the security parameters $n, k, t$ to be safe?  Or do we need to switch another code / curve entirely?
My understanding is that the attack only works against McEliece with algebraic geometry codes. The paper by Bernstein, Lange and Peters recommends parameters for McEliece with binary Goppa codes, so the attack does not apply against those parameters.