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 X X X X X X X X
0 X 0 X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 0 X X 0 X X X 2X 2X X 2X 0 0
0 0 X 2X 2X X 0 X 2X 0 X 2X X 2X 0 0 X 2X 0 X 2X X 2X 0 2X X 0 X 0 2X X 0
generates a code of length 32 over Z3[X]/(X^2) who´s minimum homogenous weight is 63.
Homogenous weight enumerator: w(x)=1x^0+52x^63+18x^66+10x^72
The gray image is a linear code over GF(3) with n=96, k=4 and d=63.
As d=63 is an upper bound for linear (96,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.00281 seconds.