The generator matrix

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

generates a code of length 80 over Z3[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+784x^144+2718x^147+4782x^150+6166x^153+7476x^156+8574x^159+8820x^162+8004x^165+6090x^168+3426x^171+1560x^174+480x^177+158x^180+6x^183+2x^189+2x^198

The gray image is a linear code over GF(3) with n=240, k=10 and d=144.
This code was found by Heurico 1.16 in 79.9 seconds.