Toric codes are a type of evaluation code introduced by J.P. Hansen in 2000. They are produced by evaluating (a vector space composed of) polynomials at the points of \((\mathbb {F}_q^*)^s\) , the monomials of these polynomials being related to a certain polytope. Toric codes related to hypersimplices are the result of the evaluation of a vector space of homogeneous monomially square-free polynomials of degree d. The dimension and minimum distance of toric codes related to hypersimplices have been determined by Jaramillo et al. in (Des Codes Cryptogr 89:269–300, 2021). The next-to-minimal weight in the case \(d = 1\) has been determined by Jaramillo-Velez et al. in (São Paulo J Math Sci 17:188– 207, 2023), and has been determined in the cases where \(3 \le d \le \frac{s - 2}{2}\) or \(\frac{s + 2}{2} \le d < s\) , by Carvalho and Patanker in 2024. In this work we characterize and determine the number of minimal (respectively, next-to-minimal) weight codewords when \(3 \le d < s\) (respectively, \(3 \le d \le \frac{s - 2}{2}\) or \(\frac{s + 2}{2} \le d < s\) ).
