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

generates a code of length 79 over Z3[X]/(X^3) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+936x^146+1788x^147+4332x^148+7512x^149+8718x^150+13758x^151+20460x^152+21346x^153+28746x^154+39084x^155+36908x^156+45060x^157+55392x^158+44398x^159+47808x^160+48966x^161+31924x^162+26976x^163+21216x^164+11364x^165+7452x^166+4206x^167+1520x^168+726x^169+378x^170+144x^171+72x^172+90x^173+52x^174+18x^175+30x^176+30x^177+6x^178+18x^179+6x^181

The gray image is a linear code over GF(3) with n=711, k=12 and d=438.
This code was found by Heurico 1.16 in 644 seconds.