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

generates a code of length 75 over Z3[X]/(X^3) who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+66x^137+166x^138+276x^140+328x^141+594x^143+780x^144+1092x^146+2326x^147+2688x^149+3662x^150+2694x^152+2640x^153+726x^155+680x^156+378x^158+148x^159+168x^161+88x^162+60x^164+52x^165+6x^167+18x^168+14x^171+12x^174+2x^177+10x^180+2x^183+2x^189+2x^192+2x^198

The gray image is a linear code over GF(3) with n=675, k=9 and d=411.
This code was found by Heurico 1.16 in 22.5 seconds.