consider a programing language that describes a program as a Turing machine operating on binary tape and ends with a filler character that must be repeated more then bb(number of states of the Turing machine described) and no character is encoded with all zeros.
let n be the number of states of a quine and q be the number of ones in the quine output.
bb(n) < q because the number of ones is at least the number of filler characters and q ≤ bb(n).
there for bb(n)<bb(n) contradiction.