The generator matrix

 1  0  0  0  0  0  1  1  1  1  0  1  1  1
 0  1  0  0  0  0  0  0  1  0  X  0  1  X
 0  0  1  0  0  0  0  1  0  1  1  0  1  X
 0  0  0  1  0  0  1  1  1  0 X+1  1 X+1  0
 0  0  0  0  1  0  1  0  0  X  0  X X+1  X
 0  0  0  0  0  1  1  0  1 X+1  1  1  X  X
 0  0  0  0  0  0  X  0  0  0  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  0
 0  0  0  0  0  0  0  0  X  X  X  0  0  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+62x^6+164x^7+371x^8+848x^9+1568x^10+2608x^11+3704x^12+4592x^13+4940x^14+4536x^15+3767x^16+2608x^17+1552x^18+880x^19+344x^20+144x^21+70x^22+4x^23+5x^24

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 3.34 seconds.