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

generates a code of length 83 over Z3[X]/(X^3) who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+60x^153+110x^156+90x^158+120x^159+144x^161+96x^162+414x^164+68x^165+4374x^166+396x^167+62x^168+342x^170+36x^171+72x^173+26x^174+46x^177+18x^180+26x^183+18x^186+8x^189+14x^192+4x^195+6x^198+6x^201+2x^204+2x^228

The gray image is a linear code over GF(3) with n=747, k=8 and d=459.
This code was found by Heurico 1.16 in 0.718 seconds.