The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 0 X X^2 X X X X^2 1 1 1 1 1 1 1 1 X X X X X X X X X X 1 1 1 1
0 X 0 X^2+X X^2 X^2+X X^2 X 0 X^2+X 0 X^2+X X^2 X X^2 X X^2+X X X^2+X X X X 0 X^2 X X 0 X^2 0 X^2 X^2+X X X^2+X X 0 X^2 X^2+X X^2+X X X 0 X^2 0 X^2 0 X^2 0 X^2
0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2
generates a code of length 48 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.
Homogenous weight enumerator: w(x)=1x^0+57x^48+2x^52+2x^56+2x^60
The gray image is a linear code over GF(2) with n=192, k=6 and d=96.
As d=96 is an upper bound for linear (192,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.0475 seconds.