The generator matrix
1 0 0 0 0 0 0 0 1 1 1 0 1 0 X 1
0 1 0 0 0 0 0 0 0 0 0 1 1 1 X X
0 0 1 0 0 0 0 0 0 0 1 0 X X 1 1
0 0 0 1 0 0 0 0 1 0 X X 1 X 1 0
0 0 0 0 1 0 0 0 1 X 0 X X+1 1 X+1 1
0 0 0 0 0 1 0 0 1 X X+1 1 0 0 X+1 X+1
0 0 0 0 0 0 1 0 1 X+1 X X+1 X+1 1 1 1
0 0 0 0 0 0 0 1 X 1 1 X+1 X 1 1 0
generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+377x^8+2020x^10+6652x^12+14592x^14+18403x^16+14184x^18+7008x^20+1952x^22+323x^24+20x^26+4x^28
The gray image is a linear code over GF(2) with n=32, k=16 and d=8.
As d=8 is an upper bound for linear (32,16,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 16.
This code was found by Heurico 1.11 in 91.3 seconds.