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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+130x^141+60x^142+6x^143+386x^144+156x^145+186x^146+558x^147+360x^148+636x^149+968x^150+1188x^151+1596x^152+2376x^153+2160x^154+2064x^155+2392x^156+1482x^157+1200x^158+466x^159+204x^160+126x^161+296x^162+168x^163+18x^164+208x^165+48x^166+144x^168+6x^169+36x^171+20x^174+16x^177+8x^180+6x^183+2x^186+2x^189+2x^195+2x^201

The gray image is a linear code over GF(3) with n=693, k=9 and d=423.
This code was found by Heurico 1.16 in 2.95 seconds.