Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch pan.
Beat cake mix, water, eggs, and oil in a large bowl with an electric mixer until combined. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes. Let cool.
Poke holes all over the cake using the handle of a wooden spoon. Whisk milk and pudding mix together in a bowl until just starting to thicken. Pour over cake, spreading with spatula to fill the holes. Refrigerate to firm, about 1 hour.
Place chocolate chips in a glass bowl. Heat heavy whipping cream in a small saucepan over medium-low heat, stirring frequently, until bubbles form, about 3 minutes. Pour over the chocolate chips; whisk until smooth. Spread chocolate ganache over cake with a spatula.