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

generates a code of length 38 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+222x^72+216x^75+216x^78+36x^81+36x^90+2x^108

The gray image is a linear code over GF(3) with n=114, k=6 and d=72.
This code was found by Heurico 1.16 in 12.3 seconds.