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  X X+1  0 X+1  0  X  0
 0  0  0  1  0  0  0  1 X+1  X  X  1  X  X  0
 0  0  0  0  1  0  1  1  0  X  X X+1  0  0  0
 0  0  0  0  0  1  1  X X+1 X+1 X+1  0 X+1  1  0
 0  0  0  0  0  0  X  0  X  0  X  X  0  0  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+110x^8+196x^9+251x^10+316x^11+604x^12+1044x^13+1100x^14+1036x^15+1033x^16+908x^17+634x^18+436x^19+284x^20+156x^21+60x^22+4x^23+16x^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 1.16 in 0.513 seconds.