Poly[N-9′-heptadecanyl-2,7-carbazole-alt-5,5-(4′,7′-di-2-thienyl-2′,1′,3′-benzothiadiazole) (PCDTBT) is a copolymer composed of alternating thiophene-benzothiadiazole-thiophene (TBT) and carbazole (Cbz) repeat units widely used for stable organic photovoltaics. However, the solubility of PCDTBT is limited, which decreases polymer yield and makes synthesis and purification tedious. Here, we introduce a strategy to increase both solubility and luminescence by the statistical incorporation of additional hexyl side chains at the TBT unit (hex-TBT). An increasing amount of hex-TBT as comonomer from 0 to 100% enhances solubility, leads to backbone torsion, and causes a blue-shift in the absorption and emission spectra. While photovoltaic performance of both PCDTBT:P3HT blends and PCDTBT:PC$\mathrm{<mrow\; data-mjx-texclass="ORD">71</mrow>}$BM blends decreases with increasing content of hex-TBT due to weaker and blue-shifted absorption, the luminescence properties can be systematically improved. Both photo- and electroluminescence (PL and EL) quantum efficiencies increase with increasing hex-TBT content. We further demonstrate solution-processed red polymer light-emitting diodes based on fully hexylated PCDTBT showing an EL quantum efficiency enhancement of up to 7 times and 2 orders of magnitude enhancement of brightness compared to standard PCDTBT. Fully hexylated PCDTBT shows a peak external quantum efficiency of 1.1% and a peak brightness of 2500 cd/m2