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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+56x^165+128x^168+96x^170+112x^171+132x^173+76x^174+402x^176+70x^177+4374x^178+444x^179+80x^180+300x^182+32x^183+84x^185+32x^186+24x^189+38x^192+22x^195+18x^198+4x^201+14x^204+8x^207+6x^210+4x^213+2x^219+2x^246

The gray image is a linear code over GF(3) with n=801, k=8 and d=495.
This code was found by Heurico 1.16 in 0.829 seconds.