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

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+202x^153+614x^156+692x^159+162x^160+1980x^162+972x^163+4968x^165+1944x^166+4940x^168+1296x^169+792x^171+506x^174+288x^177+174x^180+78x^183+24x^186+24x^189+8x^192+12x^195+2x^198+2x^204+2x^225

The gray image is a linear code over GF(3) with n=747, k=9 and d=459.
This code was found by Heurico 1.16 in 3.27 seconds.