The generator matrix

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

generates a code of length 75 over Z3[X]/(X^3) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+238x^144+48x^145+1008x^146+834x^147+192x^148+792x^149+1076x^150+138x^151+324x^152+752x^153+96x^154+720x^155+226x^156+6x^157+72x^158+20x^159+6x^160+6x^162+2x^177+2x^189+2x^192

The gray image is a linear code over GF(3) with n=675, k=8 and d=432.
This code was found by Heurico 1.16 in 0.297 seconds.