This paper considers a Gaussian multi-input multi-output (MIMO) wiretap channel with a legitimate transmitter, a legitimate receiver (Bob), an eavesdropper (Eve), and a cooperative jammer. All nodes may be equipped with multiple antennas. Traditionally, the jammer transmits Gaussian noise (GN) to enhance the security. However, using this approach, the jamming signal interferes not only with Eve but also with Bob. In this paper, besides the GN strategy, we assume that the jammer can also choose to use the encoded jammer (EJ) strategy, i.e., instead of GN, it transmits a codeword from an appropriate codebook. In certain conditions, the EJ scheme enables Bob to decode the jamming codeword and thus cancel the interference, while Eve remains unable to do so even if it knows all the codebooks. We first derive an inner bound on the system's secrecy rate under the strong secrecy metric, and then consider the maximization this bound through precoder design in a computationally efficient manner. In the single-input multi-output (SIMO) case, we prove that although non-convex, the power control problems can be optimally solved for both GN and EJ schemes. In the MIMO case, we propose to solve the problems using the matrix simultaneous diagonalization (SD) technique, which requires quite a low computational complexity. Simulation results show that by introducing a cooperative jammer with coding capability, and allowing it to switch between the GN and EJ schemes, a dramatic increase in the secrecy rate can be achieved. In addition, the proposed algorithms can significantly outperform the current state of the art benchmarks in terms of both secrecy rate and computation time.