The generator matrix

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

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+163x^8+1092x^10+3138x^12+7728x^14+8535x^16+7640x^18+3324x^20+944x^22+197x^24+4x^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 1.16 in 5.21 seconds.