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In this paper, we investigate the relationship between the profiles of Hadamard matrices and the weights of the doubly even self-orthogonal/dual \([n, m, d]\) codes from Hadamard matrices of order \(n = 8t\) with \(t \geq 1\). We show that such codes have \(m \leq \frac{n}{2}\), and give some computational results of doubly even self-orthogonal/dual \([n,m,d]\) codes from Hadamard matrices of order \(n = 8t\), with \(1 \leq t \leq 9\).