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  1  X X+1  0  0
 0  0  1  0  0  0  0  0  1  X  0  0  1  1
 0  0  0  1  0  0  0  0  1 X+1  1  X  0  0
 0  0  0  0  1  0  0  1  0  1  0 X+1  X  0
 0  0  0  0  0  1  0  1  0  X X+1 X+1  0  0
 0  0  0  0  0  0  1  1 X+1  1  X  0  1  0
 0  0  0  0  0  0  0  X  X  0  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+61x^6+140x^7+464x^8+716x^9+1597x^10+2628x^11+3748x^12+4748x^13+4682x^14+4636x^15+3653x^16+2628x^17+1666x^18+780x^19+452x^20+100x^21+57x^22+8x^23+2x^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 1.11 in 0.505 seconds.