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

generates a code of length 70 over Z3[X]/(X^3) who´s minimum homogenous weight is 132.

Homogenous weight enumerator: w(x)=1x^0+74x^132+170x^135+170x^138+1458x^140+104x^141+72x^144+62x^147+42x^150+10x^153+2x^156+10x^159+4x^162+4x^168+4x^171

The gray image is a linear code over GF(3) with n=630, k=7 and d=396.
This code was found by Heurico 1.16 in 0.163 seconds.