The generator matrix

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

generates a code of length 82 over Z3[X]/(X^3) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+84x^150+180x^152+222x^153+324x^154+822x^155+822x^156+1710x^157+1806x^158+1996x^159+3222x^160+4692x^161+3546x^162+6300x^163+6300x^164+4400x^165+6390x^166+5502x^167+3010x^168+3258x^169+1944x^170+952x^171+666x^172+438x^173+92x^174+144x^176+66x^177+42x^179+48x^180+22x^183+16x^186+8x^189+8x^192+4x^195+2x^198+2x^201+8x^204

The gray image is a linear code over GF(3) with n=738, k=10 and d=450.
This code was found by Heurico 1.16 in 13.1 seconds.