This paper studies families of self-orthogonal codes over
$\Z_4$. We show that the simplex codes (Type $\alpha$ and Type $\beta$)
We partially answer the question of $\Z_4$-linearity for the
codes from projective planes of even order.
A new family of self-orthogonal codes over
$\Z_4$ is constructed via projective planes of odd order.
Properties such as shadow
codes, self-orthogonality, weight distribution, etc. are studied.
Finally, some self-orthogonal codes constructed from twistulant
matrices are presented.