You can find Quartz deposits on the islands.
You can also get Quartz by exchanging the Sign Collection. You can find items from the Sign Collection in the Secret Treasure, or send Treasure Hunters looking for them.
The Big Liberty Statues on the Lilliput Island and the Towers and Walls on the Troy Island give away useful materials and items, including Quartz. Please, note that the Liberty Statues on the Lilliput Island and the Liberty on The Big Land/Love Island are different types of buildings.
Upon reaching level 44, you can buy and build Towers that offer you to win Quartz.
You can also get Quartz from the Legend's Set at Henry's Shop on Tortuga. To unlock this set, reach Rank 20 first.
Also, feel free to check our Facebook page - you can find a lot of valuable info about the game (and also about Quartz) there: http://fb.com/ZombieCastaways/