The risk of occurrence of atypical phenomena is a cross-cutting concern in several areas, such as engineering, climatology, finance, actuarial, among others. Extreme value theory is the natural tool to approach this theme. Many of these random phenomena carry variables defined in time and space, usually modeled through random fields. Thus, the study of random fields in the context of extreme values becomes imperative and has been developed especially in the last decade. In this work, we propose a new random field, called pMAX, designed for modeling extremes. We analyze its dependence and pre-asymptotic dependence structure through the corresponding bivariate tail dependence coefficients. Estimators for the model parameters are obtained and their finite sample properties analyzed. Examples with simulations illustrate the results.