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

generates a code of length 72 over Z3[X]/(X^2) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+32x^138+54x^141+570x^144+38x^147+18x^150+12x^153+2x^156+2x^216

The gray image is a linear code over GF(3) with n=216, k=6 and d=138.
This code was found by Heurico 1.16 in 0.0858 seconds.