Brainteaser 1575: Quantum scales

From The Sunday Times, 15th November 1992 [link]

The merchants of Mathematica only ever have to weigh things that weigh a whole number of “quantums”, that country’s unit of weight. They have a pair of balancing scales, and four weights. By using these weights (on either side of the balance) they can determine the weight of items weighing 1, 2, 3, 4, 5, … quantums, and they have designed the four weights so that this sequence continues as high as it possibly can with just four weights.

With their balance and weights they can determine the weight of a Maxpack, but not of anything heavier.

What is the weight of a Maxpack?

This puzzle was selected for the book Brainteasers (2002, edited by Victor Bryant). The wording above is taken from the book. It is slightly changed from the original puzzle, which removes an ambiguity in the original puzzle.