A subset F of a finite transitive group G ≤ Sym(Ω) is intersecting if any two elements of F agree on an element of Ω. The intersection density of G is the number ρ(G) = max |F | |G|/|Ω| | F ⊂ G is intersecting . Recently, Hujdurović et al. [11] disproved a conjecture of Meagher et al. [21, Conjecture 6.6 (3)]by constructing equidistant cyclic codes which yield transitive groups of degree pq, where p = q k −1 q−1 and q are odd primes, and whose intersection density equal to q.In this paper, we use the cyclic codes given by Hujdurović et al. and their permutation automorphisms to construct a family of transitive groups G of degree pq with ρ(G) = q k , whenever k < q < p = q k −1 q−1 are odd primes. Moreover, we extend their construction using cyclic codes of higher dimension to obtain a new family of transitive groups of degree a product of two odd primes q < p = q k −1 q−1 , and whose intersection density are equal to q. Finally, we prove that if G ≤ Sym(Ω) of degree a product of two arbitrary odd primes p > q and ω∈Ω Gω is a proper subgroup, then ρ(G) ∈ {1, q}.