Toric codes are linear error-correcting evaluation codes obtained from an integral convex polytope \(P \subset \mathbb{R}^n\) and a finite field \(\mathbb{F}\). In this paper, the authors obtain upper and lower bounds on the minimum distance of a toric code constructed from a polygon \(P \subset \mathbb{R}^2\). In many cases, the authors are able to compute this minimum distance exactly with a simple formula, under a mild condition on the size of \(\mathbb{F}\). Though the dimensions of these codes is barely mentioned in this paper, that topic was discussed in other papers, so there are many interesting and new results in this paper [see for example, J. Hansen, Appl. Algebra Eng. Commun. Comput. 13, No. 4, 289–300 (2002; Zbl 1043.94022), D. Joyner, Appl. Algebra Eng. Commun. Comput. 15, No. 1, 63–79 (2004; Zbl 1092.94031), D. Ruano, On the parameters of \(r\)-dimensional toric codes, arXiv:math/0512285; On the structure of generalized toric codes, arXiv:cs/0611010].