The generator matrix
1 0 0 1 1 1 0 1 1 0 1 0 1 X X 1 1 0 0
0 1 0 1 0 1 1 0 0 X 1 1 X+1 1 1 X+1 X 0 0
0 0 1 1 1 0 1 0 1 1 1 X 0 X+1 1 0 1 1 1
0 0 0 X 0 0 0 0 0 0 X 0 X X 0 X 0 0 X
0 0 0 0 X 0 0 0 0 X X 0 X 0 0 X 0 X 0
0 0 0 0 0 X 0 0 0 0 0 0 0 X X X X X 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 X X 0 X X
0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X X
0 0 0 0 0 0 0 0 X X X 0 0 X X X X 0 X
generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+109x^12+272x^14+683x^16+912x^18+1146x^20+560x^22+338x^24+48x^26+25x^28+2x^32
The gray image is a linear code over GF(2) with n=38, k=12 and d=12.
This code was found by Heurico 1.16 in 0.243 seconds.