Homomorphic encryption schemes emerged as the solution to the problem of secure data processing in the cloud. A fully homomorphic encryption scheme is constructed by using a Bootstrappable somewhat homomorphic encryption scheme, i.e. an encryption scheme that can homomorphically evaluate its own decryption circuit. In this paper, a somewhat homomorphic encryption scheme, based on lattices, is implemented and used for executing morphological operations over encrypted binary images. Moreover, a quantitative study to verify the influence of the implemented scheme's parameters on the execution times (key generation, encryption, decryption and morphological operations) and on the number of operations that the scheme is able to perform without leaving the decryption radius is performed.