Hi, I was wondering if anyone could help me solve this question from a past paper:

Let C be the code with parity check matrix:

$\displaystyle \begin{pmatrix}0 0 0 1 1 1 1 0 \\ 0 1 1 0 0 1 1 0 \\ 1 0 1 0 1 0 1 0 \\ 1 1 1 1 1 1 1 1 \\ \end{pmatrix}$

Prove that C is self dual. (You can assume that the dual of an (n,k)-code is an (n,n-k) code and that)

What is d for this code?

I have worked out that the matrix times by its transpose is equal to 0 to show it is orthogonal but I am unsure where to go from here