  In this work, we study the DNA codes from the ring R = Z4 + wZ4, where w^2 =
2+2w with 16 elements. We establish a one to one correspondence between the
elements of the ring R and all the DNA codewords of length 2 by defining a
distance-preserving Gau map phi. Using this map, we give several new classes of
the DNA codes which satisfies reverse and reverse complement constraints. Some
of the constructed DNA codes are optimal.
