Extract one unique SBox from Canonical Representative
This illustrates the idea with no efficiencies considered. Take the canonical Sbox, and let $$X:=[X[1],\ldots,X[16]]$$
be the vectors in $\{0,1\}^4$ in the order given by the canonical Sbox map.

Looping through all invertible $4\times4$ matrices $M_0,M_i$ and all constant vectors $c_0,c_i$ compute the list of column matrices
$$
F(M_0,M_i,c_0,c_i):=M_0 \cdot [M_i\cdot(X[1]\oplus c_i),M_i\cdot(X[2]\oplus c_i), \ldots M_i\cdot(X[16]\oplus c_i)]\oplus [c_0,\ldots,c_0],
$$
and you will find the target Sboxes for some $F$ computed during this process.

See extract from the paper quoted in the question below: