Generate $4\times 4$ Sboxes with a given branch number
The differential branch number is the sum of hamming weight between input and output difference distribution table (DDT). it is similar to linear branch number. 

One way to construct S-box with branch number 3 is to use concept of differential-equivalence, DDT-equivalence and the $\gamma$-equivalence as shown in paper "Two Notions of Differential Equivalence on Sboxes". 

The new paper accepted "Reconstructing an S-box from its Difference Distribution Table " provides algorithm to reconstruct S-box . therefore, you could apply the concept on  $\gamma$-equivalence DDT to find S-Box with branch number as you want.