Improve or verify the best-known binary constant-weight code A(29,8,7): current bounds 344 ≤ A ≤ 617

$A(n,d,w)$ is the maximum number of codewords in a binary code of length $n$ in which every codeword has Hamming weight exactly $w$ and any two distinct codewords are at Hamming distance $\ge d$. For $(n,d,w)=(29,8,7)$ the exact value is unknown: the best-known construction gives $A(29,8,7) \ge 344$ and the best upper bound is $617$, i.e. $344 \le A(29,8,7) \le 617$. Question: construct a binary constant-weight code with parameters $(29,8,7)$ and more than $344$ codewords (a new record), or independently verify that the recorded best-known construction attains exactly $344$ codewords with all constraints satisfied.

Acceptance. FULLY RESOLVES (improve): an explicit list of $> 344$ binary vectors of length $29$, each of Hamming weight exactly $7$, with all pairwise Hamming distances $\ge 8$ — verified by exhaustive pairwise check (a new lower-bound record); a code of size $617$ would settle the cell. PARTIAL: independently re-verify, with a re-runnable script, that the recorded best-known construction is a valid $(29,8,7)$ constant-weight code of size $344$ (all weights $=7$, all pairwise distances $\ge 8$). Provide the codeword list and verifier.