The palindromization map $��$ in a free monoid $A^*$ was introduced in 1997 by the first author in the case of a binary alphabet $A$, and later extended by other authors to arbitrary alphabets. Acting on infinite words, $��$ generates the class of standard episturmian words, including standard Arnoux-Rauzy words. In this paper we generalize the palindromization map, starting with a given code $X$ over $A$. The new map $��_X$ maps $X^*$ to the set $PAL$ of palindromes of $A^*$. In this way some properties of $��$ are lost and some are saved in a weak form. When $X$ has a finite deciphering delay one can extend $��_X$ to $X^��$, generating a class of infinite words much wider than standard episturmian words. For a finite and maximal code $X$ over $A$, we give a suitable generalization of standard Arnoux-Rauzy words, called $X$-AR words. We prove that any $X$-AR word is a morphic image of a standard Arnoux-Rauzy word and we determine some suitable linear lower and upper bounds to its factor complexity. For any code $X$ we say that $��_X$ is conservative when $��_X(X^{*})\subseteq X^{*}$. We study conservative maps $��_X$ and conditions on $X$ assuring that $��_X$ is conservative. We also investigate the special case of morphic-conservative maps $��_{X}$, i.e., maps such that $��\circ ��= ��_X\circ ��$ for an injective morphism $��$. Finally, we generalize $��_X$ by replacing palindromic closure with $��$-palindromic closure, where $��$ is any involutory antimorphism of $A^*$. This yields an extension of the class of $��$-standard words introduced by the authors in 2006.

Final version, accepted for publication on Theoret. Comput. Sci