Row-deletion conjecture for normalized Hadamard matrices

A normalized Hadamard matrix of order $n$ is a Hadamard matrix whose normalization is as used in the source. For a non-negative integer $r$ and a matrix $A$, let $A_{-r}$ be the submatrix obtained by deleting the first $r$ rows of $A$. A subset of a Hamming cube is diametrically-maximal if it is maximal subject to having the prescribed diameter. Row-deletion conjecture. For every non-negative integer $r$, there is a number $n_0$ such that whenever $H$ is a normalized Hadamard matrix of order $n\geq n_0$, the columns of $H_{-r}$ form a diametrically-maximal subset of $Q_{n-r}$. The source notes that this extends the verified cases obtained by deleting zero or one row, while the general assertion remains open.