The generator matrix

 1  0  1  1  1  0  1  1  1  1  1  1  X  1  1
 0  1  1  0  1  1  0  0  0  0  0  0  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  0  0
 0  0  0  0  0  0  0  0  0  0  0  X  X  0  0

generates a code of length 15 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+74x^4+64x^6+731x^8+456x^10+2792x^12+3744x^14+5031x^16+1648x^18+1314x^20+224x^22+285x^24+8x^26+12x^28

The gray image is a linear code over GF(2) with n=30, k=14 and d=4.
This code was found by Heurico 1.16 in 0.556 seconds.