The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  0  0  1
 0  1  0  0  0  0  0  0  0  0  0  1  X  X  1  1
 0  0  1  0  0  0  0  0  1  1  X  1 X+1  0 X+1  0
 0  0  0  1  0  0  0  0  1  X X+1  1  1  1  1  1
 0  0  0  0  1  0  0  0  1 X+1  1  0  0  X  1  1
 0  0  0  0  0  1  0  1  0  1  X X+1  0 X+1  1  0
 0  0  0  0  0  0  1  1 X+1  1  0  X  X X+1  1  0
 0  0  0  0  0  0  0  X  X  0  0  0  X  0  X  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+193x^8+1014x^10+3346x^12+7080x^14+9539x^16+6996x^18+3388x^20+1032x^22+171x^24+6x^26+2x^28

The gray image is a linear code over GF(2) with n=32, k=15 and d=8.
As d=8 is an upper bound for linear (32,15,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 15.
This code was found by Heurico 1.11 in 3.53 seconds.