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 X X X X X X X X 1 1 1 1 1 1 0 0 0 0 1 1 1
0 X 0 X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 X X X 0 2X 2X 2X 0 0 X X 0 X X X X 0 2X 2X 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 0 X 2X X 2X X 0 2X 0 X 2X 0 X 2X X 2X 0 0 X 2X X 0 X 0
generates a code of length 48 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.
Homogenous weight enumerator: w(x)=1x^0+60x^96+12x^99+6x^102+2x^108
The gray image is a linear code over GF(3) with n=144, k=4 and d=96.
As d=96 is an upper bound for linear (144,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.013 seconds.