This paper presents a genetic algorithm (GA) for simultaneously learning the structure and parameters of Bayesian Networks (BNs) from data. The proposed method encodes both components in a single individual, using the Minimum Description Length (MDL) principle as fitness function. The algorithm is evaluated in terms of classification accuracy and complexity across different datasets. Additionally, it is assessed based on its ability to approximate known gold-standard networks. The results suggest that this approach can obtain less complex networks while preserving an acceptable level of classification accuracy and achieving a closer structural approximation to the gold standard network.