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

generates a code of length 71 over Z3[X]/(X^3) who�s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+34x^138+78x^139+78x^140+124x^141+1644x^142+60x^143+56x^144+42x^145+24x^146+20x^147+18x^148+6x^150+2x^213

The gray image is a linear code over GF(3) with n=639, k=7 and d=414.
This code was found by Heurico 1.16 in 0.152 seconds.