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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+84x^141+132x^142+282x^143+414x^144+366x^145+486x^146+714x^147+840x^148+1386x^149+1282x^150+2118x^151+3606x^152+1896x^153+2256x^154+1482x^155+560x^156+270x^157+198x^158+284x^159+174x^160+138x^161+174x^162+90x^163+114x^164+116x^165+42x^166+54x^167+48x^168+24x^169+24x^170+12x^171+6x^172+6x^173+2x^174+2x^207

The gray image is a linear code over GF(3) with n=684, k=9 and d=423.
This code was found by Heurico 1.16 in 2.46 seconds.