The generator matrix

 1  0  0  1  1  1  1  1  1 2X  1  1  1  0 2X  1  X  1  1  X  1  1  1  1  X  1  1  1  1  1  0  1  0  1 2X 2X  1  1  0  1 2X  1  1  1  1  X  1  1  1  X  1  1  1  1  0  1  X 2X  1  1  X  1  1  1  1  1  1  1  1 2X  0  1  1  1 2X  0  1  1  1  1
 0  1  0 2X  1 2X+1  2  0 X+2  1 2X+2 2X+1 X+2  1  1  2  1 X+1  X  1 2X+2  0  1  2  0 2X+1 2X 2X+2  X 2X  1  2  1 X+1 2X  1  0  X 2X  1  1 X+1 2X+2  X  1  1 2X+1 2X 2X+2  1 X+1  1 2X+2  2  1  2  1  1 X+1 2X+1  1  1 2X+2 X+2 X+1  2  0 X+2 X+2  1  1 2X X+2 X+1  X  1 X+2 2X  0  2
 0  0  1 2X+1  1 2X 2X+2  2  X  1 X+2  2 X+1  2  X  X  1 2X+1 X+1 2X+2 2X  X  0  1  1 2X+2 X+2  0  0  1  X 2X+1 X+1 X+1  1 2X+2 X+2 2X  1  X X+1 X+2 X+1 2X+1 2X+1  2  X 2X+2  2  0  2 2X 2X+2  2 2X+1 X+2  X  0 2X+2  0 2X+1 X+2  1 2X+1 2X X+1 X+1 2X+2 X+2 2X 2X  X  1  0  1  1  2 X+1 2X 2X

generates a code of length 80 over Z3[X]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+66x^156+186x^157+100x^159+180x^160+34x^162+90x^163+12x^165+12x^166+12x^168+2x^171+18x^172+6x^174+8x^177+2x^189

The gray image is a linear code over GF(3) with n=240, k=6 and d=156.
This code was found by Heurico 1.16 in 0.0672 seconds.