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

generates a code of length 91 over Z3[X]/(X^3) who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+166x^174+84x^175+54x^176+276x^177+672x^178+216x^179+246x^180+1458x^181+216x^182+1580x^183+1002x^184+108x^186+78x^187+122x^189+46x^192+48x^193+84x^195+60x^196+18x^198+24x^201+2x^264

The gray image is a linear code over GF(3) with n=819, k=8 and d=522.
This code was found by Heurico 1.16 in 49.6 seconds.