The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  1  X  1
 0  1  0  0  0  0  0  0  0  0  0  1  X  X  1 X+1
 0  0  1  0  0  0  0  0  1  X X+1  1 X+1  0  X X+1
 0  0  0  1  0  0  0  0  1 X+1  1  0  X  0  1  X
 0  0  0  0  1  0  0  0  1  1  X  1 X+1 X+1  0  1
 0  0  0  0  0  1  0  1  1  0 X+1  X  0 X+1 X+1  X
 0  0  0  0  0  0  1  1  X  0  1 X+1  0  0  X X+1
 0  0  0  0  0  0  0  X  0  X  X  X  0  X  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+143x^8+156x^9+624x^10+884x^11+1764x^12+2556x^13+3408x^14+4596x^15+4504x^16+4596x^17+3408x^18+2556x^19+1764x^20+884x^21+624x^22+156x^23+143x^24+1x^32

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 7.29 seconds.