The generator matrix

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

generates a code of length 15 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+251x^8+440x^9+330x^10+360x^11+1336x^12+2392x^13+2272x^14+1864x^15+1959x^16+2088x^17+1380x^18+824x^19+536x^20+200x^21+112x^22+24x^23+13x^24+2x^26

The gray image is a linear code over GF(2) with n=30, k=14 and d=8.
As d=8 is an upper bound for linear (30,14,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 14.
This code was found by Heurico 1.10 in 0.813 seconds.