The generator matrix

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

generates a code of length 15 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+35x^6+32x^7+251x^8+328x^9+1047x^10+1496x^11+2656x^12+3848x^13+4198x^14+5016x^15+4207x^16+3736x^17+2662x^18+1608x^19+1040x^20+280x^21+247x^22+40x^23+37x^24+3x^26

The gray image is a linear code over GF(2) with n=30, k=15 and d=6.
This code was found by Heurico 1.16 in 2.97 seconds.