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

generates a code of length 70 over Z3[X]/(X^2) who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+114x^137+26x^138+36x^141+4x^144+42x^146+8x^147+4x^153+6x^155+2x^156

The gray image is a linear code over GF(3) with n=210, k=5 and d=137.
This code was found by Heurico 1.16 in 1.02 seconds.