Heidegger's idea here is actually not difficult to make out, unlikely as that might appear, if we trace the quotation to its source and check the context. Gavin Rae, 'Overcoming Philosophy: Heidegger, Metaphysics, and the Transformation to Thinking', Human Studies, Vol. 36, No. 2 (Summer 2013), pp. 235-257 : 247 :
In The Word of Nietzsche: 'God is Dead,' Heidegger claims thought must move
away from emphasising objective conceptualisation to take seriously alternative,
non-conceptual modes of thinking. As he puts it, 'thinking begins only when we
have come to know that reason, glorified for centuries, is the most stiff-necked
adversary of thought' (1977: 61). Similarly, in What is Called Thinking?,
Heidegger claims being is not capable of being understood if we start with the
notion that only conceptual thought counts as knowledge (1968: 179). Heidegger
wants to not only open thought to alternative, non-conceptual modes of thinking, but
to also get thought to recognise these alternatives are legitimate and justified. As
being 'is' universal, fluid, dynamic, and historical so too must thought move in these
directions. Only by recognising, opening itself to, and taking seriously non
conceptual thinking will thought be able to engage with being on being's own terms.
Only non-philosophy, which does not entail a valorisation of science or any other
so-called humanity, but genuine, meditative thinking, can open thought to being in
the way that does not impose itself on being and reveals being as being reveals itself
to thought (Krzystof 2008 : 251)
In other words, Heidegger's view is that 'being' cannot be understood solely through conceptual thought, with which he identifies reason. Non-conceptual ways of thinking are also requisite. Being is too 'fluid, dynamic, and historical' to be captured, penetrated, by static, inflexible conceptual thinking. This is hardly unambiguously clear but Heidegger's broad point is one that we can make some sense of.
To make fuller sense of Heidegger's mind here you would need to probe his notions of being, thought, and the conceptual. That's certainly a task for another time.
Heidegger, M. (1977). The word of Nietzsche: "god is dead". In The question concerning technology & other essays (pp. 53-114) (W. Lovitt, Trans.). New York: Harper Perennial. (Originally published in 1949).
Heidegger, M. (1968). What is called thinking? (J. G. Gray. Trans.). New York: Harper Perennial. (Originally published in 1954).
Krzysztof, Z. (2008). The return to philosophy? or: Heidegger and the task of thinking. Journal of the British Society for Phenomenology, 59(3), 249-259.
Gavin Rae, 'Overcoming Philosophy: Heidegger, Metaphysics, and the Transformation to Thinking', Human Studies, Vol. 36, No. 2 (Summer 2013), pp. 235-257.