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  X
 0 X^2  0  0  0  0  0  0  0  0 2X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 2X^2  0  0 X^2 X^2 2X^2 X^2  0  0  0 X^2  0 2X^2 X^2 2X^2 X^2 2X^2 X^2 2X^2  0 2X^2  0 X^2 2X^2 2X^2 2X^2 X^2  0 2X^2  0 X^2  0 X^2 2X^2 X^2  0  0 2X^2 2X^2 2X^2  0 X^2 2X^2 2X^2 2X^2 2X^2  0 X^2 2X^2  0 X^2 2X^2  0
 0  0 X^2  0  0  0 X^2 X^2 X^2 2X^2  0 X^2 2X^2 X^2 X^2 2X^2 2X^2  0 X^2 X^2  0 X^2  0 2X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 2X^2  0  0 X^2 X^2  0 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2  0  0 2X^2  0 X^2  0 2X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2  0 2X^2 2X^2 2X^2  0
 0  0  0 X^2  0 X^2 2X^2 2X^2 X^2 2X^2  0  0 2X^2 2X^2  0  0 X^2 X^2 X^2 2X^2 X^2 X^2 X^2 2X^2  0 2X^2 X^2  0 2X^2 2X^2 2X^2 2X^2  0  0 X^2 2X^2  0 2X^2  0  0 X^2 2X^2 2X^2 X^2  0 2X^2  0  0 2X^2 X^2 X^2 X^2 X^2 2X^2 X^2  0  0 2X^2  0 2X^2  0 2X^2 2X^2  0  0 2X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2
 0  0  0  0 X^2 2X^2 2X^2  0 2X^2 2X^2 X^2 X^2 2X^2 X^2  0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2  0 2X^2  0 X^2 2X^2  0 2X^2  0 X^2  0 X^2 X^2 2X^2 X^2  0  0 X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2  0  0  0  0 2X^2 X^2 X^2  0 X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2  0  0  0 X^2 2X^2  0  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+60x^141+222x^144+1458x^146+378x^147+42x^150+18x^153+6x^159+2x^216

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 0.187 seconds.