The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 X X
0 0 X 0 0 0 0 0 0 0 0 0 X X X
0 0 0 X 0 0 0 0 0 0 0 0 X 0 X
0 0 0 0 X 0 0 0 0 0 0 0 X X 0
0 0 0 0 0 X 0 0 0 0 0 X X X X
0 0 0 0 0 0 X 0 0 0 0 X 0 0 X
0 0 0 0 0 0 0 X 0 0 0 X 0 X X
0 0 0 0 0 0 0 0 X 0 0 X 0 X 0
0 0 0 0 0 0 0 0 0 X 0 X X 0 0
0 0 0 0 0 0 0 0 0 0 X X X 0 X
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+35x^6+105x^8+168x^10+280x^12+435x^14+2048x^15+435x^16+280x^18+168x^20+105x^22+35x^24+1x^30
The gray image is a linear code over GF(2) with n=30, k=12 and d=6.
This code was found by Heurico 1.16 in 1.77 seconds.