With bounded receive buffers, the aggregate bandwidth of multipath transmission degrades significantly in the presence of path heterogeneity. The performance could even be worse than that of single-path TCP, undermining the advantage gained by using multipath transmit. Furthermore, multipath transmission also suffers from delay and jitter even with large receive buffers. In order to tolerate the path heterogeneity when the receive buffer is bounded, we propose a new multipath TCP protocol, namely SC-MPTCP, by integrating linear systematic coding into MPTCP. In SC-MPTCP, we make use of coded packets as redundancy to counter against expensive retransmissions. The redundancy is provisioned into both proactive and reactive data. Specifically, to send a generation of packets, SC-MPTCP transmits proactive redundancy first and then delivers the original packets, instead of encoding all sent-out packets as all the existing coding solutions have done. The proactive redundancy is continuously updated according to the estimated aggregate retransmission ratio. In order to avoid the proactive redundancy being underestimated, the pre-blocking warning mechanism is utilized to retrieve the reactive redundancy from the sender. We use an NS-3 network simulator to evaluate the performance of SC-MPTCP with and without the coupled congestion control option. The results show that with bounded receive buffers, MPTCP achieves less than 20% of the optimal goodput with diverse packet losses, whereas SC-MPTCP approaches the optimal performance with significantly smaller receive buffers. With the help of systematic coding, SC-MPTCP reduces the average buffer delay of MPTCP by at least 80% in different test scenarios. We also demonstrate that the use of systematic coding could significantly reduce the arithmetic complexity compared with the use of non-systematic coding.