Best way to arrange 16 dice in a 4x4 cell grid

[ruby83]

A player is given a set of 16 random dice to place on a 4x4 cell grid.

Dice placement in certain combinations (rows or columns only) can you score points.

One Pair 1 point (e.g. 3,3)
Two Pairs 3 points (e.g. 2,2,5,5)
Triple 4 points (e.g. 4,4,4)
Straight (any order) 5 points (e.g. 1,2,3,4 or 5,3,6,4)
Quadruple 8 points 1,1,1,1

The player gets a random dice at each turn, so it should be impossible to get all dice of the same (to make 8 quads). So, what is the next (best) arrangement that can score maximum points with a set of random dice?

The playing grid is here:
http://rubysoft.com.my/pirates_playground.php

[gen2]

8 quads is NOT impossible (unless the program is designed to reject such combinations). The chance of getting 16 dice coming up with the same number is 1 in 6^15 (i in 470 184 984 576).

Obviously the next best would be 15 showing the same number and the 16th one different scoring 6 quads and 2 triples = 56 points