  In this paper, we prove a lower bound on the soundness of quantum locally
testable codes under the distance balancing construction of Evra et al.
arXiv:2004.07935 [quant-ph]. Our technical contribution is that the new
soundness of the quantum code is at least the old soundness divided by the
classical code length (up to a constant factor). This allows us to use any
classical code with independent checks when distance balancing, where
previously only the repetition code had been considered for qLTCs. By using a
good classical LDPC code, we are able to grow the dimension of the hypersphere
product codes arXiv:1608.05089 [quant-ph] and the hemicubic codes
arXiv:1911.03069 [quant-ph] while maintaining their distance and locality, but
at the expense of soundness. From this, and also by distance balancing a chain
complex of Cross et al. arXiv:2209.11405 [cs.IT], we obtain quantum locally
testable codes of new parameters.
