The generator matrix

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

generates a code of length 75 over Z3[X]/(X^3) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+378x^147+72x^148+108x^149+1278x^150+72x^151+54x^152+18x^153+18x^154+180x^156+2x^162+6x^171

The gray image is a linear code over GF(3) with n=675, k=7 and d=441.
This code was found by Heurico 1.16 in 0.168 seconds.