The generator matrix
1 0 1 1 1 1 1 0 1 1 1 1 X 1 1 X
0 1 1 2 2X+1 0 2 1 X X 2X+1 X+2 1 X+1 X+2 1
0 0 2X 0 X X 2X 2X X 0 2X 2X 0 X 0 2X
generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 30.
Homogenous weight enumerator: w(x)=1x^0+112x^30+96x^33+32x^36+2x^48
The gray image is a linear code over GF(3) with n=48, k=5 and d=30.
As d=30 is an upper bound for linear (48,5,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.000839 seconds.