In [IEEE Trans. Inf. Theory 40, 1003--1012 (1994; Zbl 0814.94027)] \textit{G. L. Feng} and \textit{T. R. N. Rao} proposed a construction of algebraic-geometric codes without algebraic geometry, by using only rings of polynomials. They also gave a bound on the minimum distance of the obtained codes, the so-called Feng-Rao bound. These ideas were later formalized by \textit{T. Høholdt}, \textit{J. H. van Lint} and \textit{R. Pellikaan} [Algebraic geometry codes, in: Handbook of coding theory, 871--961 (1998; Zbl 0922.94015)]. In this paper, the authors show two classes of codes for which the Feng-Rao bound equals the true minimum distance. The first class is obtained by using a curve \(G(X)+H(Y)=0\) where \(\deg G\) and \(\deg H\) are coprime. These curves belong to the family of Type I curves introduced by Feng and Rao. The second class is formed by some codes defined on the rational points in \(\mathbb{F}_4^m\) of the intersection of Hermitian surfaces \(X_i^3+X_{i +1} ^2+X_{i+1}= 0\), \(i=1,\dots,m-1\).