The generator matrix

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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 142.

Homogenous weight enumerator: w(x)=1x^0+66x^142+138x^144+318x^145+378x^146+706x^147+900x^148+1152x^149+2414x^150+1614x^151+3582x^152+4904x^153+2676x^154+6444x^155+7046x^156+3702x^157+6624x^158+6246x^159+2382x^160+3384x^161+2156x^162+1086x^163+306x^164+264x^165+258x^166+62x^168+96x^169+48x^171+24x^172+14x^174+14x^177+10x^180+12x^183+10x^186+6x^189+2x^192+2x^195+2x^201

The gray image is a linear code over GF(3) with n=702, k=10 and d=426.
This code was found by Heurico 1.16 in 46.7 seconds.