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

generates a code of length 70 over Z3[X]/(X^3) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+48x^136+78x^137+40x^138+168x^139+1638x^140+24x^141+72x^142+54x^143+14x^144+24x^145+12x^146+12x^148+2x^210

The gray image is a linear code over GF(3) with n=630, k=7 and d=408.
This code was found by Heurico 1.16 in 0.144 seconds.