The generator matrix

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

generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+97x^6+98x^7+501x^8+664x^9+1645x^10+2536x^11+3680x^12+4904x^13+4578x^14+4876x^15+3555x^16+2536x^17+1778x^18+680x^19+448x^20+88x^21+93x^22+2x^23+7x^24+1x^26

The gray image is a linear code over GF(2) with n=28, k=15 and d=6.
As d=6 is an upper bound for linear (28,15,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 15.
This code was found by Heurico 1.16 in 3.66 seconds.