The generator matrix

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

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+244x^72+240x^75+90x^78+78x^81+48x^84+18x^87+10x^90

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 0.00855 seconds.