The generator matrix

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

generates a code of length 16 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+175x^10+485x^12+811x^14+1086x^16+945x^18+447x^20+113x^22+29x^24+4x^26

The gray image is a linear code over GF(2) with n=32, k=12 and d=10.
As d=10 is an upper bound for linear (32,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12.
This code was found by Heurico 1.16 in 0.273 seconds.