Underwater multistatic sonar cooperative detection faces the issue that distant sonars fail to capture target echoes. This paper proposes a networkcodingaided multistatic multicast system with relaysonar assistance for underwater acoustic networks. Relay sonars forward activesonardetected target data to remote sonars and apply network coding prior to forwarding to cut retransmissions and boost transmission efficiency. To mitigate latency in traditional opportunisticlisteningbased network coding, a feedbackdriven proactive coding scheme is adopted: remote sonars feed back receivedpacket indexes, enabling relays to proactively encode complementary missing packets. A throughput analytical model is built to derive closedform expressions under maximum encodingnumber constraints for arbitrary remotesonar quantities. Simulations reveal prominent networkcoding gains at moderate packetloss rates. In highloss scenarios, the scheme improves throughput efficiency by 30%60%, outperforming schemes without network coding or relays and supporting reliable, bandwidthsaving underwater acoustic transmission.