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

generates a code of length 75 over Z3[X]/(X^3) who´s minimum homogenous weight is 143.

Homogenous weight enumerator: w(x)=1x^0+252x^143+250x^144+72x^145+534x^146+126x^147+594x^148+1200x^149+606x^150+1188x^151+1062x^152+66x^153+90x^154+162x^155+52x^156+54x^158+18x^159+84x^161+80x^162+42x^164+6x^167+6x^168+6x^170+8x^171+2x^210

The gray image is a linear code over GF(3) with n=675, k=8 and d=429.
This code was found by Heurico 1.16 in 1.12 seconds.