It depends on whether the verb “grow” is used transitively or intransitively.
“Let’s grow” can mean “let us grow [ourselves]”, intransitively. In that sense “Let’s grow good,” is ungrammatical, since the adverb to modify “how we grow” should be “well” and not “good”.
However, it is possible, I think, to “grow [the] good”, using “grow” as a transitive verb (and “good” as a noun), even if the construction is unusual and maybe a little awkward. For comparison, “Be well” means ”[You] be healthy”, but “Be good” means ”[You] be a good person”. Those are not at all unusual or awkward uses.
So on that basis, “Let’s grow good” as a way of saying “Let us grow goodness” is not bad at all, as @ragingloli suggests. I don’t particularly like it, because it is going to appear incorrect to most literate English speakers, but it could be correct in this sense, at least. Still awkward.