The generator matrix

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

generates a code of length 88 over Z3[X]/(X^3) who´s minimum homogenous weight is 167.

Homogenous weight enumerator: w(x)=1x^0+234x^167+202x^168+918x^169+912x^170+694x^171+1926x^172+1104x^173+734x^174+2286x^175+1308x^176+934x^177+3186x^178+1380x^179+788x^180+1692x^181+642x^182+204x^183+198x^184+114x^185+32x^186+66x^188+34x^189+72x^191+12x^192+4x^198+4x^201+2x^213

The gray image is a linear code over GF(3) with n=792, k=9 and d=501.
This code was found by Heurico 1.16 in 1.83 seconds.