The carbon efficiency of manufacturing industry is receiving more and more attention. An effective way to improve the carbon efficiency of manufacturing industry is to design a scheduling strategy aimed at reducing the energy cost of the production process. This paper investigates the carbon-efficient distributed heterogeneous shop scheduling problem for factories with different processing capacities, with productivity-related (makespan) and sustainability-related (total carbon emission, TCE) indicators as objectives. A multi-objective variable-scale evolutionary strategy (MOVES) is proposed to optimize two objectives simultaneously. First, a dynamic ruin intensity method is designed. Second, a carbon emission saving method based on problem knowledge is designed to optimize carbon emissions. Finally, a local search method is designed to further optimize makespan and TCE. Numerical experiments demonstrate the effectiveness of the proposed algorithm.