The generator matrix

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

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+98x^8+80x^9+261x^10+348x^11+644x^12+960x^13+1056x^14+1324x^15+1017x^16+944x^17+658x^18+372x^19+276x^20+64x^21+72x^22+4x^23+12x^24+1x^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 0.415 seconds.