The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  1  1  X  1
 0  X  0  0  0  0  0  0  0  0  X  0  X  X  0
 0  0  X  0  0  0  0  0  0  0  X  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  X  X  0  X  0
 0  0  0  0  X  0  0  0  0  X  X  0  0  X  0
 0  0  0  0  0  X  0  0  0  X  0  0  X  X  0
 0  0  0  0  0  0  X  0  0  X  0  X  0  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  X  0
 0  0  0  0  0  0  0  0  X  X  X  0  X  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+55x^8+22x^10+96x^12+128x^13+72x^14+256x^15+87x^16+128x^17+116x^18+16x^20+40x^22+1x^24+6x^26

The gray image is a linear code over GF(2) with n=30, k=10 and d=8.
This code was found by Heurico 1.16 in 0.0121 seconds.