The generator matrix
1 0 0 1 1 1 0 1 1 0 1 1 X X 1
0 1 0 1 0 1 1 0 0 X 1 1 1 1 0
0 0 1 1 1 0 1 0 1 1 1 X 0 1 0
0 0 0 X 0 0 0 0 0 0 0 X X X 0
0 0 0 0 X 0 0 0 0 X 0 X X 0 0
0 0 0 0 0 X 0 0 0 0 X 0 X X 0
0 0 0 0 0 0 X 0 0 0 X X X 0 0
0 0 0 0 0 0 0 X 0 X 0 X 0 X 0
0 0 0 0 0 0 0 0 X X X 0 0 X 0
generates a code of length 15 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+71x^8+32x^9+182x^10+192x^11+288x^12+480x^13+472x^14+640x^15+487x^16+480x^17+308x^18+192x^19+176x^20+32x^21+56x^22+1x^24+6x^26
The gray image is a linear code over GF(2) with n=30, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0887 seconds.