The generator matrix

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

generates a code of length 15 over Z2[X]/(X^2) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+68x^7+214x^8+466x^9+917x^10+1596x^11+2596x^12+3684x^13+4460x^14+4788x^15+4465x^16+3592x^17+2606x^18+1684x^19+916x^20+444x^21+204x^22+56x^23+6x^25+5x^26

The gray image is a linear code over GF(2) with n=30, k=15 and d=7.
This code was found by Heurico 1.16 in 5.23 seconds.