The relation between the length and the minimum distance of four dimensional binary self-orthogonal codes are discussed. The nonexistence of self-orthogonal codes with parameters \[ 15m + 5, 4, 8m + 2 \] and that with parameters \[ 15m + 12, 4, 8m + 6 \] are proved, thus for each n ≥ 8, the minimum distance dso of optimal \[n, 4 \] self - orthogonal is determined. At last, for each n≥ 8 a generator matrix that generates a \[n, 4, dso (n) \] self-orthogonal code is presented, and their weight polynomials are determined.