In this paper, we show that the smallest length for which there is an extremal ternary self-dual code with a trivial automorphism group is 28 by constructing such a code of length 28. This code is the first example of extremal ternary self-dual codes with trivial automorphism groups. An extremal ternary self-dual [32, 16, 9] code with a trivial automorphism group is also constructed. A 32-dimensional odd unimodular lattice with minimum norm 3 and a trivial automorphism group is obtained from the code by Construction A.
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