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

generates a code of length 83 over Z3[X]/(X^3) who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+110x^153+72x^154+168x^155+702x^156+690x^157+726x^158+1532x^159+2112x^160+1656x^161+3552x^162+4884x^163+3750x^164+5362x^165+6906x^166+4380x^167+5596x^168+6276x^169+2862x^170+3128x^171+2100x^172+942x^173+776x^174+180x^175+78x^176+152x^177+90x^178+18x^179+130x^180+18x^181+38x^183+6x^186+10x^189+22x^192+4x^195+6x^198+12x^201+2x^207

The gray image is a linear code over GF(3) with n=747, k=10 and d=459.
This code was found by Heurico 1.16 in 13.4 seconds.