This paper addresses precoder design for secure multiple-input multiple-output (MIMO) integrated sensing and communications (ISAC) systems. We introduce a MIMO channel with a multiple-antenna eavesdropper and a multiple-antenna sensing receiver (MIMO-ME-MS) and analyze the fundamental performance limits of this tripartite tradeoff. Using sensing mutual information, we formulate the precoder design as a nonconvex weighted sum rate maximization problem. A high signal-to-noise ratio analysis based on a subspace decomposition characterizes the maximum weighted degrees of freedom. This analysis reveals the structure of a quasi-optimal precoder that must span the “useful subspace” and demonstrates the inadequacy of extending known schemes from simpler wiretap or ISAC channels. To solve this nonconvex problem, we develop a practical two-stage iterative algorithm that alternates between a sequential basis construction stage and a power allocation stage that solves the resulting difference-of-convex program. We demonstrate that the proposed method captures the desirable precoder structure identified in our analysis and achieves substantial performance gains in the MIMO-ME-MS channel.