To understand which part of the brain contains primarily white matter, we must recall the functional and structural differences between white matter and gray matter. White matter is composed mainly of \emph{myelinated nerve fibers}, which act as communication highways between different brain regions. Gray matter, in contrast, contains neuronal cell bodies that perform signal processing, memory formation, and computation.
The \emph{cerebral cortex} (option A) consists mostly of gray matter and is involved in higher-order processing such as cognition, reasoning, memory, and voluntary movement. The \emph{basal ganglia} (option B) are deep gray matter nuclei involved in motor control and coordination. The \emph{limbic system} (option C) also primarily contains gray matter structures responsible for emotions, learning, and memory.
However, the \emph{corpus callosum} (option D) is made of a large bundle of myelinated axons that connect the left and right cerebral hemispheres. It facilitates inter-hemispheric communication and is therefore predominantly white matter. Because of this, it is the only option that fits the requirement of a structure composed mainly of white matter.
Thus, the correct answer is (D) Corpus callosum.