<p>A hierarchical poset code’s hull is defined as its intersection with its dual. Linear codes with small dimensions have significant potential for applications in the algorithmic aspects of codes in both classical and quantum coding theory. This study investigates the existence and construction of hierarchical poset codes with small hull dimensions over finite fields. Motivated by the significance of Linear Complementary Dual (LCD) codes in cryptographic and quantum error-correcting applications, we explore hierarchical poset metrics as a natural generalization of the Hamming metric, enabling more structured and flexible coding frameworks. We establish theoretical results characterizing the hull dimension of hierarchical poset codes and present canonical and systematic forms that facilitate their construction. In particular, we provide explicit constructions of hierarchical poset codes with one-dimensional and zero-dimensional hulls that meet the Griesmer like bound, thereby achieving optimality in terms of both length and minimum distance. Existence criteria and uniqueness conditions for these optimal codes are discussed, along with examples computed using the MAGMA system. The results demonstrate that hierarchical poset structures can yield both hull-one and LCD codes that are length-optimal, offering valuable tools for secure communications and advanced coding applications.</p>