The generator matrix

1 0 0 0 1 1 1 X 1 1 1 1 0 X 1 1
0 1 0 0 0 1 1 1 0 X 0 X+1 1 1 X 1
0 0 1 0 1 0 X+1 1 1 X X+1 X+1 X+1 1 X X+1
0 0 0 1 1 X+1 X 1 X 1 0 X X X+1 X 0
0 0 0 0 X X 0 0 0 0 X X X X X 0

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+71x^12+138x^14+126x^16+76x^18+89x^20+10x^22+1x^24

The gray image is a linear code over GF(2) with n=32, k=9 and d=12.
As d=12 is an upper bound for linear (32,9,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 9.
This code was found by Heurico 1.10 in 0 seconds.