Improve the bounds on the football-pool number K_3(6): ternary covering code of length 6, radius 1

Let $K_3(n)=K_3(n,1)$ be the minimum number of codewords in a ternary code $C \subseteq \{0,1,2\}^n$ of covering radius 1 - i.e. such that every word in $\{0,1,2\}^n$ is within Hamming distance 1 of some codeword. This is the 'football pool problem' for $n$ matches. Exact values are known for small $n$ (e.g. $K_3(3)=5$, $K_3(4)=9$). For $n=6$ the exact value is open: the best known bounds are $65 \le K_3(6) \le 73$. Exhibit a ternary covering code of length 6, radius 1, with at most 72 codewords (improving the upper bound), or prove $K_3(6) \ge 66$ (improving the lower bound).

Acceptance. FULLY RESOLVES (upper bound): an explicit list of $\le 72$ codewords in $\{0,1,2\}^6$ such that every one of the 729 words of $\{0,1,2\}^6$ is at Hamming distance $\le 1$ from a listed codeword - verified exhaustively over all 729 words. FULLY RESOLVES (lower bound): a machine-checkable proof (e.g. an ILP infeasibility / LP-bound certificate) that no radius-1 covering code of size $\le 65$ exists, i.e. $K_3(6) \ge 66$. PARTIAL: a code matching the current record (73), or any verified bound improvement. Provide the codeword list and a verifier (or the certificate).