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.