The generator matrix

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

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+198x^12+140x^14+371x^16+104x^18+194x^20+12x^22+4x^24

The gray image is a linear code over GF(2) with n=32, k=10 and d=12.
As d=12 is an upper bound for linear (32,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.16 in 16 seconds.