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

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 166.

Homogenous weight enumerator: w(x)=1x^0+192x^166+306x^168+282x^169+46x^171+726x^172+2994x^174+1386x^175+160x^177+78x^178+16x^180+60x^181+12x^183+78x^184+108x^186+108x^187+6x^190+2x^258

The gray image is a linear code over GF(3) with n=783, k=8 and d=498.
This code was found by Heurico 1.16 in 4.23 seconds.