The generator matrix

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

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+150x^6+252x^7+856x^8+1500x^9+3312x^10+5236x^11+7316x^12+9436x^13+9516x^14+9324x^15+7253x^16+5236x^17+3392x^18+1564x^19+820x^20+212x^21+142x^22+8x^23+10x^24

The gray image is a linear code over GF(2) with n=28, k=16 and d=6.
As d=6 is an upper bound for linear (28,16,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 16.
This code was found by Heurico 1.11 in 2.13 seconds.