The generator matrix
1 1 1 1 1 1 1 1 1 X 1 1 1 X X X X 0 X
0 X 0 0 0 0 0 0 X^2 X^2 X X X X X^2+X X^2 X^2+X X 0
0 0 X 0 0 0 0 X^2 X^2+X X X^2+X X X^2 X^2 X^2+X 0 X^2+X 0 X
0 0 0 X 0 0 0 X^2+X X^2 X X X^2+X X^2 0 X^2 X^2+X X^2+X X^2+X 0
0 0 0 0 X 0 X X X^2+X 0 X X^2 X X^2+X X^2 X X^2+X 0 X
0 0 0 0 0 X X X^2 X^2 X X^2+X X^2+X 0 0 X^2+X X^2 X^2+X X 0
0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2
generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+211x^12+718x^14+2201x^16+5008x^18+5102x^20+2300x^22+646x^24+160x^26+31x^28+6x^30
The gray image is a linear code over GF(2) with n=76, k=14 and d=24.
This code was found by Heurico 1.16 in 2.79 seconds.