The generator matrix

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

generates a code of length 86 over Z3[X]/(X^3) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+800x^162+342x^163+1062x^164+2430x^165+1692x^166+3222x^167+4002x^168+2682x^169+4230x^170+5854x^171+4536x^172+6210x^173+6006x^174+3708x^175+4446x^176+3174x^177+1476x^178+1116x^179+1026x^180+144x^181+126x^182+294x^183+216x^186+162x^189+72x^192+6x^195+14x^198

The gray image is a linear code over GF(3) with n=774, k=10 and d=486.
This code was found by Heurico 1.16 in 53.2 seconds.