The generator matrix

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

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+106x^8+204x^9+251x^10+308x^11+620x^12+1020x^13+1100x^14+1060x^15+1009x^16+932x^17+634x^18+412x^19+300x^20+148x^21+60x^22+12x^23+12x^24+3x^26

The gray image is a linear code over GF(2) with n=30, k=13 and d=8.
As d=8 is an upper bound for linear (30,13,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 13.
This code was found by Heurico 1.10 in 0.156 seconds.