The generator matrix

 1  0  0  1  1  1  0  1  1  0  1  1  0  X  X
 0  1  0  1  0  1  1  0  0  0  1 X+1  1  1  0
 0  0  1  1  1  0  1  0  1  1  1  0  0  1  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X
 0  0  0  0  X  0  0  0  0  0  0  X  X  X  0
 0  0  0  0  0  X  0  0  0  0  X  X  X  0  0
 0  0  0  0  0  0  X  0  0  0  X  X  X  X  X
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  X
 0  0  0  0  0  0  0  0  X  0  0  X  0  X  X
 0  0  0  0  0  0  0  0  0  X  X  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+161x^8+392x^10+1456x^12+1960x^14+2395x^16+1176x^18+560x^20+56x^22+35x^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 11.8 seconds.