I am looking for all $k$-dimensional subspaces of $(\mathbb{Z}/2\mathbb{Z})^n$ up to permutational equivalence.
Is there a database of all $[n,k]$-codes up to equivalence for reasonable values of $(n,k)$? For instance, $1 \leq k \leq 6$ and $6 \leq n \leq 12$ (giving around 35,000 codes).
When $k=1$, there are $n$ such subspaces, each uniquely determined by the Hamming weight of the nonzero element.
When $k=2$, there are 0, 1, 3, 6, 10, 16, 23, 32 … (OEIS:A034198) such subspaces.
When $k=3$, there are 0, 0, 1, 4, 10, 22, 43, 77, … (OEIS:A034357) such subspaces.
When $k=4$, there are 0, 0, 0, 1, 5, 16, 43, 106, … (OEIS:A034358) such subspaces.
For each $k\geq 2$, I have trouble finding representatives of the codes for $n \geq 8$, but surely someone has recorded them somewhere. For $n=8$, there are just 8, 32, 77, 106 such codes for $k=1,2,3,4$, so it seems reasonable to me that someone wrote them down.
I have found several databases of "good" codes, but I actually want the bad codes too.