The main subject of this dissertation is the construction of extremal Type II \(\mathbb{Z}_4\)-codes. The aim is to construct new extremal Type II \(\mathbb{Z}_4\)-codes. We constructed extremal Type II \(\mathbb{Z}_4\)-codes using known methods and methods developed in this dissertation starting from existing extremal Type II \(\mathbb{Z}_4\)-codes. We also constructed Type II \(\mathbb{Z}_4\)-codes from certain binary codes and examined the extremality of obtained codes. We have been using GAP and Magma software packages. Some necessary concepts from coding theory, design theory, graph theory and basic facts about lattices are introduced in the first chapter. Second chapter of the dissertation contains the classification of extremal Type II \(\mathbb{Z}_4\)-codes of lengths 8, 16 and 24 and information about numbers of known extremal Type II \(\mathbb{Z}_4\)-codes of larger lengths. It also contains constructions of self-dual \(\mathbb{Z}_4\)-codes and Type II \(\mathbb{Z}_4\)-codes from binary codes with certain properties. We have been trying to construct new extremal Type II \(\mathbb{Z}_4\)-codes of lengths 56 and 64 starting from some binary codes. Third chapter of the dissertation contains three constructions of extremal Type II \(\mathbb{Z}_4\)-codes from existing extremal Type II \(\mathbb{Z}_4\)-codes. We corrected errors in the first construction and obtained new extremal Type II \(\mathbb{Z}_4\)-codes of length 32 in that way. Starting from known methods for construction of extremal Type II \(\mathbb{Z}_4\)-codes of lengths 24; 32 and 40 we developed a method for construction of extremal Type II \(\mathbb{Z}_4\)-codes of lengths 48; 56 and 64. We have been trying to construct new extremal Type II \(\mathbb{Z}_4\)-codes using this method. The second construction was used to get new extremal Type II \(\mathbb{Z}_4\)-codes of length 40. We tried to construct new extremal Type II \(\mathbb{Z}_4\)-codes of lengths 56 and 64 starting from certain existing extremal Type II \(\mathbb{Z}_4\)-codes of lengths 56 and 64 using the first and the third construction in this chapter. We showed that new extremal Type II \(\mathbb{Z}_4\)-codes of lengths 56 and 64 cannot be obtained in this way. In the next part of the dissertation we looked at the binary codes associated with Hadamard matrices. Their properties were analyzed. We proved their suitability for construction of extremal Type II \(\mathbb{Z}_4\)-codes introduced in the second chapter of the dissertation. New extremal Type II \(\mathbb{Z}_4\)-codes of lengths 32 and 40 were obtained with the use of Hadamard matrices. The last, fifth chapter, is devoted to constructing combinatorial designs and graphs using supports of codewords with specific weights of the obtained new extremal Type II \(\mathbb{Z}_4\)-codes of length 32. Properties of the constructed structures were analyzed. We tried to construct new designs and distance-regular or strongly-regular graphs. Parameters of all obtained designs are known. We obtained some regular graphs which are not distance-regular.