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

generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+46x^141+24x^144+66x^147+1944x^148+60x^150+42x^156+2x^162+2x^222

The gray image is a linear code over GF(3) with n=666, k=7 and d=423.
This code was found by Heurico 1.16 in 0.195 seconds.