The generator matrix

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

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+73x^6+216x^7+568x^8+1080x^9+1930x^10+3600x^11+5376x^12+7256x^13+8490x^14+8464x^15+8353x^16+7224x^17+5356x^18+3664x^19+2008x^20+1064x^21+533x^22+184x^23+78x^24+16x^25+2x^26

The gray image is a linear code over GF(2) with n=30, k=16 and d=6.
This code was found by Heurico 1.11 in 2.01 seconds.