As a tool towards quantum error correction, additive conjucyclic codes have gained great attention. But, their algebraic structure is completely unknown over finite fields (except Fq2\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}_{q^2}$$\end{document}) as well as rings. In this article, we investigate the structure of additive conjucyclic codes over Galois rings GR(2r,2)\documentclass[12pt]{minimal}
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\begin{document}$$GR(2^r,2)$$\end{document}, where r≥2\documentclass[12pt]{minimal}
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\begin{document}$$r\ge 2$$\end{document} is an integer. We develop a one-to-one correspondence between the family of additive conjucyclic codes of length n over GR(2r,2)\documentclass[12pt]{minimal}
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\begin{document}$$GR(2^r,2)$$\end{document} and the family of linear cyclic codes of length 2n over Z2r\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {Z}}_{2^r}$$\end{document}. This correspondence helps to obtain additive conjucyclic codes over GR(2r,2)\documentclass[12pt]{minimal}
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\begin{document}$$GR(2^r,2)$$\end{document} via known linear cyclic codes over Z2r\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {Z}}_{2^r}$$\end{document}. We prove that the trace dual CTr\documentclass[12pt]{minimal}
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\begin{document}$${\mathscr {C}}^{Tr}$$\end{document} of an additive conjucyclic code C\documentclass[12pt]{minimal}
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\begin{document}$${\mathscr {C}}$$\end{document} is also an additive conjucyclic code. Moreover, we derive a necessary and sufficient condition of additive conjucyclic codes to be self-dual. We further propose a technique for constructing linear cyclic codes over Z2r\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {Z}}_{2^r}$$\end{document} contained in additive conjucyclic codes over GR(2r,2)\documentclass[12pt]{minimal}
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\begin{document}$$GR(2^r,2)$$\end{document}. Last but not least, we explicitly derive the generator matrices for these codes.
