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It has been shown by Gulliver (Discrete Math. 149 (1996) 83) that there exists a ternary [98,6,63] code. But it is unknown whether or not there exists a ternary [97,6,63] code. The purpose of this paper is to prove that there is no ternary [97,6,63] code using the structure of a {267,87;5,3}-minihyper and a generator matrix of a ternary [97,6,63] code. Since n3(6,63)=97 or 98 and d3(97,6)=62 or 63, this implies that n3(6,63)=98 and d3(97,6)=62, where n3(k,d) and d3(n,k) denote the smallest value of n and the largest value of d, respectively, for which there exists an [n,k,d] code over the Galois field GF(3). [Copyright &y& Elsevier]