The generator matrix

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

generates a code of length 86 over Z3[X]/(X^3) who´s minimum homogenous weight is 163.

Homogenous weight enumerator: w(x)=1x^0+42x^163+114x^164+26x^165+408x^166+156x^167+60x^168+66x^169+648x^170+46x^171+2976x^172+1320x^173+54x^174+168x^175+84x^176+30x^177+24x^178+16x^180+54x^181+24x^182+8x^183+126x^184+84x^185+18x^187+6x^190+2x^255

The gray image is a linear code over GF(3) with n=774, k=8 and d=489.
This code was found by Heurico 1.16 in 0.935 seconds.