Y. Matsumoto's 11/8-conjecture for smooth 4-manifolds

Let $X$ be a closed oriented smooth $4$-manifold whose intersection form is equivalent to

$$Q_X=2k(-E_8)\oplus lH.$$

Matsumoto's $11/8$-conjecture. The inequality

$$l\ge 3|k|$$

should hold. This is the stated $/8$-conjecture by Y. Matsumoto; the source provides no resolution status.