The generator matrix

1 0 0 0 0 0 1 1 1 1 0 1 X 1
0 1 0 0 0 0 0 0 1 X+1 1 X X 0
0 0 1 0 0 0 1 0 X+1 X 1 0 X 0
0 0 0 1 0 0 1 X 0 1 X+1 X 0 0
0 0 0 0 1 0 1 X+1 X X+1 0 0 1 1
0 0 0 0 0 1 X 1 X+1 0 X X+1 X+1 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+74x^8+152x^9+204x^10+208x^11+424x^12+744x^13+620x^14+480x^15+461x^16+360x^17+196x^18+80x^19+64x^20+24x^21+4x^22

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 1.10 in 0.047 seconds.