We start defining subvarieties of a toric variety that are parameterized by Laurent monomials and the corresponding toric codes. We recall their vanishing ideals and give algorithms for finding their binomial generators which will be used to compute main parameters of the corresponding toric codes. We show that these ideals are lattice ideals and give an algorithm to find a basis for the corresponding lattice. Finally, we give this lattice explicitly under a mild condition. This is a joint work with Esma Baran.