In this work, we propose jutted binary modulation on conjugate-reciprocal zeros (J-BMOCZ) for non-coherent communication under a carrier frequency offset (CFO). By introducing asymmetry to the Huffman BMOCZ zero constellation, we exploit the identical aperiodic auto-correlation function of BMOCZ sequences to derive a Fourier-domain metric for CFO estimation. Unlike the existing methods for Huffman BMOCZ, which require a cyclically permutable code (CPC) for pilot-free CFO correction, J-BMOCZ enables the estimation of a CFO without the use of pilots or channel coding. Through numerical simulations in additive white Gaussian noise and fading channels, we show that the bit error rate (BER) loss of J-BMOCZ under a CFO is just 1 dB over Huffman BMOCZ without a CFO. Furthermore, the results show that coded J-BMOCZ achieves better BER performance than Huffman BMOCZ with a CPC.