The generator matrix

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

generates a code of length 70 over Z3[X]/(X^3) who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+396x^137+120x^138+1350x^140+72x^141+42x^144+198x^146+6x^156+2x^162

The gray image is a linear code over GF(3) with n=630, k=7 and d=411.
This code was found by Heurico 1.16 in 0.132 seconds.