  We construct entire solutions of the magnetic Ginzburg-Landau equations in
dimension 4 using Lyapunov-Schmidt reduction. The zero set of these solutions
are close to the minimal submanifolds studied by Arezzo-Pacard\cite{Arezzo}. We
also show the existence of a saddle type solution to the equations, whose zero
set consists of two vertical planes in $\mathbb{R}^4$. These two types of
solutions are believed to be energy minimizers of the corresponding energy
functional and lie in the same connect component of the moduli space of entire
solutions.
