The generator matrix

 1  0  0  0  0  0  1  1  1  0  X  1  X  1  1  1
 0  1  0  0  0  0  0  0  0  0  1  X  1  1  1 X+1
 0  0  1  0  0  0  0  0  0  0  1  1  X X+1  1  1
 0  0  0  1  0  0  0  1  1  1  0  1  0  1 X+1  X
 0  0  0  0  1  0  1  1  0  1  0  0 X+1 X+1  X  0
 0  0  0  0  0  1  1  0  1  1  X X+1  0 X+1 X+1 X+1
 0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0
 0  0  0  0  0  0  0  X  0  X  X  0  0  X  0  0
 0  0  0  0  0  0  0  0  X  X  X  0  X  0  0  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+109x^8+236x^9+589x^10+888x^11+1641x^12+2568x^13+3676x^14+4536x^15+4471x^16+4416x^17+3374x^18+2600x^19+1886x^20+952x^21+540x^22+168x^23+83x^24+20x^25+13x^26+1x^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 5.62 seconds.