The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  1  1
 0  1  0  0  0  0  0  0  0  0 X+1  X X+1  1  X
 0  0  1  0  0  0  0  0  X  1 X+1  1  X  1 X+1
 0  0  0  1  0  0  0  0 X+1  1  1  0  X X+1 X+1
 0  0  0  0  1  0  0  0  1  X  1 X+1  1  1 X+1
 0  0  0  0  0  1  0  1  0 X+1  X X+1  1  0  1
 0  0  0  0  0  0  1  1  0  1 X+1  0 X+1  X  0
 0  0  0  0  0  0  0  X  X  0  X  X  0  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+58x^7+218x^8+514x^9+902x^10+1514x^11+2604x^12+3726x^13+4500x^14+4830x^15+4393x^16+3522x^17+2632x^18+1726x^19+956x^20+426x^21+156x^22+64x^23+20x^24+4x^25+2x^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 5.45 seconds.