Puzzle from Good Will Hunting

Ben's local shop stocks eggs in boxes of capacity 6, 9, or 20 eggs. What is the highest number of eggs that you CAN'T make?

For example, you can make 29 with one 9 box and one 20 box, 29=9+20,

you can make 30 with a five 6 boxes, 30=5x6.

but you can't make 31.


For those wanting an extra puzzle, can you prove that your answer is correct. Namely, all numbers higher than your chosen integer can be written as a linear combination of 6, 9 or 12.