In this paper we show that the support of the codewords of each type in the Kerdock code of length 2^m over Z_4 form 3-designs for any odd integer m \geq 3. In particular, two new infinite families of 3-designs are obtained in this construction for any odd integer m \geq 3, whose parameters arev=2^m , k= 2^{m-1} + 2^{m-2} \pm 2^{\frac{m-3}{2}}, and \lambda = \frac{k (k-1) (k-2)}{2^m-2}.