The generator matrix

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

generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+118x^8+76x^9+189x^10+288x^11+436x^12+652x^13+568x^14+672x^15+401x^16+292x^17+250x^18+64x^19+68x^20+4x^21+16x^22+1x^26

The gray image is a linear code over GF(2) with n=28, k=12 and d=8.
As d=8 is an upper bound for linear (28,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12.
This code was found by Heurico 1.16 in 0.117 seconds.