Improve or verify the best-known [80,40] linear code over GF(3): current bounds 19 ≤ d ≤ 26

A linear $[n,k]_q$ code is a $k$-dimensional subspace of $\mathbb{F}_{3}^n$; its minimum distance $d$ is the smallest Hamming weight of a nonzero codeword. For $[n,k]=[80,40]$ over $\mathbb{F}_{3}$ the largest achievable minimum distance is unknown: the best-known code has $d=19$ and the best nonexistence (upper) bound is $26$, i.e. $19 \le d_{\max}(80,40) \le 26$. The lower bound is met by an explicit best-known code (constructed via shortening of an extended quadratic-residue-based code); the upper bound is a nonexistence bound. Question: construct a linear $[80,40]_{3}$ code with minimum distance $\ge 20$ (a new record, improving the lower bound), or independently verify that the recorded best-known $[80,40,19]_{3}$ code has minimum distance exactly $19$.

Acceptance. FULLY RESOLVES (improve): a generator matrix $G\in\mathbb{F}_{3}^{40\times80}$ with $\mathrm{rank}(G)=40$ whose minimum distance $d'\ge 20$, certified by a minimum-distance computation (e.g. Brouwer–Zimmermann in Magma/GAP/SageMath); $d'=26$ would settle the cell. PARTIAL: independently recompute, with a re-runnable script, the minimum distance of the recorded best-known $[80,40,19]_{3}$ code from its generator matrix and confirm it equals $19$ (reproduction of the record). Provide $G$ and the verification code.