The problem of sending a secret message over the Gaussian multiple-input multiple-output wiretap channel is studied. In a recent work, we have proposed a layered coding scheme where a scalar wiretap code is used in each layer, and successive interference cancellation (SIC) is carried at the legitimate receiver. By a proper rate allocation across the layers, we showed that this scheme satisfies the secrecy constraint at the eavesdropper and achieves the secrecy capacity. However, the existence of the scalar codes was based upon a random coding argument. In this work we take a further step and show how the scheme can be based upon any codes that are good for the ordinary (non-secrecy) additive white Gaussian noise channel. As any stage of the SIC process is equivalent to achieving a corner point of a Gaussian multiple-access channel (MAC) capacity region, the class of codes used needs to be good for the MAC under SIC. Since in the secrecy analysis of our layered scheme, it suffices at each stage to consider a genie-aided eavesdropper that performs SIC, the coding task reduces to guaranteeing secrecy for corner points of induced MACs to the eavesdropper. Structured generation of such codes from ordinary ones is discussed.