The generator matrix

 1  0  0  0  1  1  1  0  1  1  X  1  1  1  1
 0  1  0  0  0  1  1  1  0  X  0  X X+1 X+1  X
 0  0  1  0  1  1  0  1  0  1  1 X+1  0  1  0
 0  0  0  1  1  0  1  1  1  0  1  X  0 X+1  1
 0  0  0  0  X  0  0  0  0  0  X  X  X  X  X
 0  0  0  0  0  X  0  0  0  X  X  X  X  0  X
 0  0  0  0  0  0  X  0  0  X  X  0  X  0  0
 0  0  0  0  0  0  0  X  0  X  X  0  X  X  X
 0  0  0  0  0  0  0  0  X  0  X  0  0  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+109x^8+468x^10+1228x^12+2324x^14+2223x^16+1244x^18+516x^20+60x^22+19x^24

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 0.377 seconds.