Indeterminacy locus of an Iitaka fibration

Question

This might be a trivial question, in this case I apologize. Let $X$ be a smooth projective complex algebraic variety of dimension $n$ and Kodaira dimension $n-1$. Let $\phi:X\dashrightarrow Z$ be the Iitaka fibration, i.e. the rational map induced by the linear system $|mK_X|$ for $m$ divisible enough. When $n=2$ then the indeterminacy locus of $\phi$ is a divisor, hence after extending $\phi$ in codimension one we obtain a legit morphism to $Z$. Does the same hold in general?