The generator matrix
1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 0 1 1 0 1 X^2+X 1 1 1 X^2+X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 X X^2 X^2 X X X^2
0 1 X+1 X^2+X X^2+1 1 0 X+1 1 X^2+X X^2+1 1 0 X+1 1 X^2+X X+1 1 X^2+1 1 0 X^2+X X^2+1 1 X^2 X X^2 X X^2 X X^2 X X^2+X+1 1 X^2+X+1 1 X^2+X+1 1 X^2+X+1 1 1 1 1 1 1 1 1
0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2
0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2
generates a code of length 47 over Z2[X]/(X^3) who´s minimum homogenous weight is 46.
Homogenous weight enumerator: w(x)=1x^0+30x^46+192x^47+30x^48+2x^62+1x^64
The gray image is a linear code over GF(2) with n=188, k=8 and d=92.
As d=93 is an upper bound for linear (188,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.0358 seconds.