Self-dual \(\mathbb{Z}_4\)-codes are, depending on their Euclidean weight distribution, divided on Type I and Type II codes. For self-dual \(\mathbb{Z}_4\)-codes, a theoretical upper bound on the minimum Euclidean weight of a code is known. Codes that meet that upper bound are called extremal \(\mathbb{Z}_4\)-codes. It is known that Type I extremal \(\mathbb{Z}_4\)-codes do not exist for lengths 24 and 48. For these lengths, self-dual \(\mathbb{Z}_4\)-codes that have the best possible minimum weight are called near-extremal \(\mathbb{Z}_4\)-codes. The main subject of this thesis are extremal and near-extremal \(\mathbb{Z}_4\)-codes. It is known that Type II \(\mathbb{Z}_4\)-codes exist only for lengths divisible by 8. Since we wanted to construct \(\mathbb{Z}_4\)-codes of Type I and Type II, our work is restricted to such lengths. The known method of construction of a self-dual \(\mathbb{Z}_4\)-code has a doubly-even binary code of dimension \(k\) as a starting point. It consists of choosing one matrix \(B\) among the \(2^{\frac{k(k+1)}{2}}\) binary \(k \times k\) matrices that are suitable for the construction of a self-dual \(\mathbb{Z}_4\)-code. The usual approach to the construction of extremal or near-extremal \(\mathbb{Z}_4\)-codes consists of the construction of self-dual \(\mathbb{Z}_4\)-codes and checking their minimum Euclidean weight. The calculation of the minimum Euclidean weight is necessary to determine extremality or near-extremality of \(\mathbb{Z}_4\)-codes, but it is also time consuming. Calculation of minimum Euclidean weight of the code gets slower as the length of the examined code gets bigger. This fact, together with the size of the search space, makes this method inefficient. In this thesis, we modified the known method in such way that more than one \(\mathbb{Z}_4\)-code can be checked for extremality or near-extremality, from one calculation of the minimum Euclidean weight. This increases the efficiency of the existing method. Also, we developed a method to construct a series of Hadamard designs on \(4n - 1\) points from one skew-symmetric Hadamard matrix of order \(n\). This was motivated by the known fact that incidence matrix of a Hadamard 3- design spans a doubly-even binary code. We used developed algorithms to construct new extremal \(\mathbb{Z}_4\)-codes of length 32 and 40. Also, we used the residue codes of the known extremal \(\mathbb{Z}_4\)-codes of length 40 to construct new extremal \(\mathbb{Z}_4\)-codes of the same length. Regarding length 48, by our modified method, we obtained already known extremal \(\mathbb{Z}_4\)-code, and at least two nonequivalent near-extremal \(\mathbb{Z}_4\)-codes. This near-extremal \(\mathbb{Z}_4\)-codes are of no great importance since they have the same residue code as the already known extremal \(\mathbb{Z}_4\)-code of that length. We applied described methods on codes of lengths 56, 64 and 72, but no extremal or near-extremal \(\mathbb{Z}_4\)-codes were constructed. From obtained codes of length 32 and 40, we constructed strongly regular graphs. All of the obtained graphs were already known. Also, we constructed 1-designs on 32 points from obtained extremal \(\mathbb{Z}_4\)-codes of length 32. Some of the constructed designs are resolvable.