We present new wide-field weak lensing mass maps for the Year 1 Dark Energy Survey data, generated via a forward fitting approach. This method of producing maps does not impose any prior constraints on the mass distribution to be reconstructed. The technique is found to improve the map reconstruction on the edges of the field compared to the conventional Kaiser-Squires method, which applies a direct inversion on the data; our approach is in good agreement with the previous direct approach in the central regions of the footprint. The mapping technique is assessed and verified with tests on simulations; together with the Kaiser-Squires method, the technique is then applied to data from the Dark Energy Survey Year 1 data and the differences between the two methods are compared. We also produce the first DES measurements of the convergence Minkowski functionals and compare them to those measured in simulations.