The generator matrix

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

generates a code of length 80 over Z3[X]/(X^3) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+1242x^148+1782x^149+4178x^150+7326x^151+9396x^152+13988x^153+20070x^154+20718x^155+29400x^156+38880x^157+37932x^158+44598x^159+54510x^160+45522x^161+46686x^162+47340x^163+32166x^164+27226x^165+21498x^166+11412x^167+7670x^168+4494x^169+1764x^170+856x^171+402x^172+120x^173+62x^174+48x^175+30x^176+44x^177+36x^178+18x^179+8x^180+12x^181+6x^182

The gray image is a linear code over GF(3) with n=720, k=12 and d=444.
This code was found by Heurico 1.16 in 653 seconds.