Problem 11 (1994 AIME)

Ninety-four bricks, each measuring $4''\times 10''\times 19''$, are to be stacked one on top of another to form a tower 94 bricks tall. Each brick can be oriented so it contributes $4''\,$ or $10''\,$ or $19''\,$ to the total height of the tower. How many different tower heights can be achieved using all of the ninety-four bricks?