Chemical evolution models predict a gradual build-up of 13C in the Universe, based on empirical nuclear reaction rates and assumptions on the properties of stellar populations. However, old metal-poor stars within the Galaxy contain more 13C than is predicted, suggesting that further refinements to the models are necessary. Gas at high-redshift provides important supplementary information at metallicities $-2\lesssim \left[{\rm Fe/H}\right]\lesssim -1$, for which there are only a few measurements in the Galaxy. We obtained new, high-quality, VLT/ESPRESSO observations of the QSO B1331$+$170 and used them to measure 12C/13C in the damped Lyman-$\alpha$ system (DLA) at $z_{\rm abs}=1.776$, with $\left[{\rm Fe/H}\right]$ = -1.27. AI-VPFIT, an artificial intelligence tool based on genetic algorithms and guided by a spectroscopic information criterion, was used to explore different possible kinematic structures of the carbon gas. Three hundred independent AI-VPFIT models of the absorption system were produced using pre-set 12C/13C values, ranging from 4 to 500. Our results show that ${\rm ^{12}C / ^{13}C}=28.5^{+51.5}_{-10.4}$, suggesting a possibility of 13C production at low metallicity.