Let \( L_1, L_2 \) be the lines passing through the point \( P(0,1) \) and touching the parabola \( 9x^2 + 12x + 18y - 14 = 0 \). Let \( Q \) and \( R \) be the points on the lines \( L_1 \) and \( L_2 \) such that the \( \triangle PQR \) is an isosceles triangle with base \( QR \). If the slopes of the lines \( QR \) are \( m_1 \) and \( m_2 \), then \( 16\left(m_1^2 + m_2^2\right) \) is equal to ____.
