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 X
0 X 0 0 X 0 X X 2X 0 0 X X 0 2X X 2X 2X 0 X 2X 0 X 2X 2X 2X 2X 0 0 0 X X 0 X X 2X X
0 0 X 0 2X X 2X X 2X 0 X X 0 2X 0 0 X X 2X 2X 2X 2X X 0 0 X 2X 0 0 X 2X X X 2X 0 2X 0
0 0 0 X 2X 2X 0 2X 2X 2X X 0 2X 0 2X X X 0 X X X 2X X 0 X 2X 0 0 X 2X 2X 2X X X X 2X 2X
generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.
Homogenous weight enumerator: w(x)=1x^0+114x^72+108x^75+18x^81+2x^108
The gray image is a linear code over GF(3) with n=111, k=5 and d=72.
This code was found by Heurico 1.16 in 0.00708 seconds.