One of the most prominent properties of dinoflagellates is their large sized and highly chromosome-laden nucleus, which contains dozens of cylindrically shaped chromosomes. With such high chromatic concentration, these chromosomes condense into ordered helical structures and were claimed to be responsible for the large circular polarization effects observed in the light scattering from dinoflagellates. In previous research, a thin helix model of a chromosome was used to compare the Discrete Dipole Approximation (DDA) and the analytical Born approximation calculations. However, for such a simplified model only modest qualitative agreements with experimental measurements were achieved. Moreover, only one chromosome in one nucleus was simulated, overlooking the effects of interactions between chromosomes. In this work, we adopt the helical plywood liquid crystal model with a capsule shape, in which parallel fibrils lie in plains perpendicular to the helix axis and the orientations of these fibrils twist at a constant angle between two neighboring layers. The ADDA code is applied to calculate the 16 Mueller matrix elements of light scattering from a single chromosome and from the nucleus, which is composed of a collection of randomly positioned and randomly orientated chromosomes. Special attention is paid to the S14 Mueller matrix element, which describes the ability of differentiating left and right circularly polarized light. Our results show that large S14 back scattering signals from the dinoflagellate nucleus results from the underlying helical structures of its chromosomes. These signals are sensitive to the light wavelength and pitch of the chromatic helix, the latter of which is species specific. Therefore, detecting back scattering S14 signal could be a promising method to monitor dinoflagellates such as Karenia brevis, the causal agent of the Florida red tide.