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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+954x^144+1614x^145+3660x^146+7064x^147+9702x^148+14646x^149+18514x^150+23280x^151+28512x^152+34912x^153+41448x^154+46536x^155+49960x^156+49896x^157+48012x^158+43432x^159+36090x^160+27720x^161+19840x^162+11490x^163+7140x^164+3966x^165+1734x^166+558x^167+322x^168+156x^169+72x^170+72x^171+24x^172+48x^173+36x^174+12x^175+18x^177

The gray image is a linear code over GF(3) with n=702, k=12 and d=432.
This code was found by Heurico 1.16 in 638 seconds.