"deeply rooted," 1590s, literally "dyed with grain "cochineal," the red dyestuff (see engrain). Figuratively, "thoroughly imbued" (of habits, principles, prejudices, etc.) from 1851. In reference to dyed carpets, etc., it is attested from 1766, from the manufacturing phrase in (the) grain "in the raw material before manufacture."
ingrained habits of a lifetime
inglorious
in-going
ingot
ingraft
ingrain
ingrained
ingrate
ingratiate
ingratiation
ingratitude
ingrave