The generator matrix
1 1 1 1 1 1 1 1 1 X 1 1 1 X 1
0 X 0 0 0 0 0 0 0 0 X 0 X X 0
0 0 X 0 0 0 0 0 0 0 X X X 0 0
0 0 0 X 0 0 0 0 0 0 X X 0 X 0
0 0 0 0 X 0 0 0 0 X X 0 0 X 0
0 0 0 0 0 X 0 0 0 X 0 0 X X 0
0 0 0 0 0 0 X 0 0 X 0 X 0 X 0
0 0 0 0 0 0 0 X 0 X X X X X 0
0 0 0 0 0 0 0 0 X X X 0 X 0 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+55x^8+22x^10+96x^12+128x^13+72x^14+256x^15+87x^16+128x^17+116x^18+16x^20+40x^22+1x^24+6x^26
The gray image is a linear code over GF(2) with n=30, k=10 and d=8.
This code was found by Heurico 1.16 in 0.0121 seconds.