Pyth, 18 bytes

c4.PC"H#ût"_S16

Run the code.

c4.PC"H#ût"_S16

    C"H#ût"       Convert the packed string to the number 1122196781940
  .P       _S16   Take that-numbered permutation of the reversed range [16,15,...,1]
c4                Chop into piece of length 4

Reversing the range was meant to lower the permutation index, since the output starts with 16, but I think it only broke even.

Pyth, 18 bytes

c4.PC"H#ût"_S16

Run the code.

c4.PC"H#ût"_S16

    C"H#ût"       Convert the packed string to the number 1122196781940
  .P       _S16   Take that-numbered permutation of the reversed range [16,15,...,1]
c4                Chop into piece of length 4

Reversing the range was meant to lower the permutation index, since the output starts with 16, but I think it only broke even.

This beat out a more boring strategy of converting the table directly to base 17 and then a string (link) for 20 bytes:

c4jC"úz(ás¸H"17