Does swapping rows of a parity check matrix affect the corresponding linear code?
$$ H= \begin{bmatrix} 1 & 0 & 1 & 0 & 1 & 0 & 1\\ 1 & 1 & 0 & 0 & 1 & 1 & 0\\ 1 & 1 & 1 & 1 & 0 & 0 & 0\\ \end{bmatrix} $$
$$H^{\prime} = \begin{bmatrix} 1 & 1 & 0 & 0 & 1 & 1 & 0\\ 1 & 0 & 1 & 0 & 1 & 0 & 1\\ 1 & 1 & 1 & 1 & 0 & 0 & 0\\ \end{bmatrix} $$
Well, permuting rows does not effect the linear code, since the rows of the generator matrix generate the code (likewise, the rows of the parity check matrix generate the dual code). The code will be the same, since the order of the generators does not matter.
The dual code is just the orthogonal complement $C^\perp$ of the given code $C$ as a linear vector space. Coding theory has its own terminology here.
The story is different if the columns are permuted. Then the coordinate positions of the code are permuted and the resulting code is permutation equivalent to the original code (and has the same parameters).