Add a voltage offset to a resistor ladder R-2R
May sound odd but just an idea:

Connect the leftmost 2R's one end to 0.3VDC instead of GND. And use 0.3VDC as logic-0 instead of 0V. This will offset the zero scale output to 0.3VDC. And the output voltage will be \$V_o = (Vref-0.3V)\cdot [code]/255\$.