The sum rate performance of quantized precoding using Gibbs sampling is evaluated in a massive multiple-input multiple-output (MIMO) system in this paper. The massive MIMO is a promising technique to improve spectrum efficiency and energy efficiency. In a full digital massive MIMO system, however, the resolution of digital-to-analogue converters (DACs) in transmit antenna branches have to be low enough because of their power consumption. Therefore, quantized precoding or precoding with the low resolution DACs is investigated. A conventional optimization criterion minimizes errors between a desired received signal and a designed signal. However, the system sum rate may decrease as it increases transmit power. This paper proposes two optimization criteria that take not only the errors but also the transmit power into account to select the candidate quantized transmit signal in order to maximize the sum rate. Moreover, Gibbs sampling is applied to obtain the suboptimal solution of the optimization problem. Numerical results obtained through computer simulation show that the proposed sum rate based criterion for the optimization achieves the approximately 1.3 times higher sum rate than the conventional criterion on a Rician fading channel. On the other hand, the proposed symbol-power-to-mean-square-error ratio (SMSER) based criterion shows faster optimization convergence.