A set of laser beams carrying orbital angular momentum is designed with the objective of establishing an effective underwater communication link. Messages are constructed using unique Laguerre-Gauss beams, which can be combined to represent four bits of information. We report on the experimental results where the beams are transmitted through highly turbid water, reaching approximately 12 attenuation lengths. We measured the signal-to-noise ratio in each test scenario to provide characterization of the underwater environment. A convolutional neural network was developed to decode the received images with the objective of successfully classifying messages quickly. We demonstrate near-perfect classification in all scenarios, provided the training set includes some images taken under the same underwater conditions.