In this paper, we characterize the performance of relay-assisted underwater wireless optical code division multiple access (OCDMA) networks over turbulent channels. In addition to scattering and absorption effects of underwater channels, we also consider optical turbulence as a log-normal fading coefficient in our analysis. To simultaneously and asynchronously share medium among many users, we assign a unique optical orthogonal code (OOC) to each user in order to actualize OCDMA-based underwater network. The most significant challenge in underwater optical communication is in the ability to extend the short range of its coverage. In order to expand the viable communication range, we consider multi-hop transmission to the destination. Moreover, we evaluate the performance of a relay-assisted point-to-point UWOC system as a special case of the proposed relay-assisted OCDMA network. Our numerical results indicate significant performance improvement by employing intermediate relays, e.g., one can achieve $32$ {dB} improvement in the bit error rate (BER) of $10^{-6}$ using only a dual-hop transmission in a $90$ {m} point-to-point clear ocean link.