The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  X  1  1  1
 0  1  0  0  1  0  0  1  1  0  0  0  0  0  0
 0  0  1  0  1  0  1  0  1  0  0  0  0  0  0
 0  0  0  1  1  1  0  0  1  0  0  0  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  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+103x^4+336x^6+1466x^8+128x^9+2075x^10+1280x^11+2574x^12+3968x^13+1637x^14+5632x^15+1637x^16+3968x^17+2574x^18+1280x^19+2075x^20+128x^21+1466x^22+336x^24+103x^26+1x^30

The gray image is a linear code over GF(2) with n=30, k=15 and d=4.
This code was found by Heurico 1.16 in 1.66 seconds.