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

generates a code of length 73 over Z3[X]/(X^3) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+26x^141+72x^143+90x^144+1836x^146+88x^147+10x^150+36x^152+26x^153+2x^219

The gray image is a linear code over GF(3) with n=657, k=7 and d=423.
This code was found by Heurico 1.16 in 0.216 seconds.