The neural tube (Fig. 1) is the embryo's precursor to the central nervous system, which comprises the brain and spinal cord. Its structure can be described in standard anatomical terms of location and their respective axes.
The dorsal - ventral axis (back to abdominal side) can be visualized by dissecting the neural tube transversely (Fig. 2). This axis is important for development. In the spinal cord, for instance, the dorsal region is the place where the spinal neurons receive input from sensory neurons, while the ventral region is where the motor neurons reside. In the middle are numerous interneurons that relay information between them. The polarity of the neural tube is induced by signals coming from its immediate environment. The dorsal pattern is imposed by the epidermis, while the ventral pattern is induced by the notochord (Gilbert, 2000).
Conversely, the anterior - posterior axis (head to tail) can be seen by a longitudinal transection (Fig. 1). Here, the important regions of the brain can be identified; the neural tube balloons into three primary vesicles, namely the forebrain (prosencephalon), midbrain (mesencephalon), and hindbrain (rhombencephalon). The prosencephalon becomes subdivided into the anterior telencephalon and the more caudal diencephalon (Gilbert, 2000).
Hence, regarding your question - there exists no such thing as a dorsal ventral cord.

Fig. 1. Anterior-to-posterior axis of the neural tube. Early primary structures (left) and adult structures (right). source: Gilbert (2000).

Fig. 2. Dorsal-ventral axis of the neural tube. source: Gilbert (2000).
Reference
- Gilbert, Developmental Biology. 6th ed. Sunderland (MA): Sinauer Associates (2000)