The generator matrix

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

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+120x^6+753x^8+3120x^10+7448x^12+9888x^14+7427x^16+3152x^18+744x^20+104x^22+11x^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 5.5 seconds.