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We present our ALMA Band 8 observations of a damped Ly$α$ absorption (DLA) system at $z$=3.150 observed in the spectrum of the quasar Q2233+131 at $z$=3.295. The optical counterpart of this DLA has been identified and it shows a double-peaked Ly$α$ emission line. Since one possible origin of DLAs at high redshift is an outflowing gas from star-forming galaxies, DLA2233+131 provides a good laboratory to investigate the nature of high-$z$ DLAs. Motivated by this, we have carried out ALMA band 8 observations to study the [C II] line in this system. However, we do not detect any significant emission line in the observed pass bands. Instead, we have serendipitously found three submm continuum sources in the observed sky area. One appears to be the quasar Q2233+131 itself while the other two sources are newly identified submm galaxies (SMGs), called SMG1 and SMG2 in this paper. They are located at a separation of 400.7 and 800.1 from Q2233+131, respectively. Their 646 $μ$m fluxes are 6.35 mJy and 6.43 mJy, respectively, being higher than that of Q2233+131, 3.62 mJy. Since these two SMGs are not detected in the optical images obtained with the Hubble Space Telescope and the Subaru Telescope, they have a very red spectral energy distribution. It is, therefore,suggested that they are high-redshift galaxies or very dusty galaxies at intermediate redshift although we cannot rule out the possibility that they are optically very faint SMG analogs at low redshift. Follow up observations will be necessary to explore the nature of this interesting region.