The generator matrix

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

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+146x^10+489x^12+790x^14+1185x^16+926x^18+414x^20+122x^22+22x^24+1x^28

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 0.284 seconds.