The generator matrix
1 0 1 1 1 X^2 1 1 0 1 1 X 1 1 0 1 1 X X^2
0 1 1 0 X+1 1 1 0 1 X^2 X+1 1 X^2+X+1 X 1 X X+1 1 0
0 0 X 0 0 X^2 0 X^2+X X^2+X X^2+X X^2+X X^2 X X^2+X X 0 X^2 X X
0 0 0 X X^2 X X^2+X X^2+X X^2+X X^2 X X^2+X X^2 0 X^2 X X X^2 X
generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+221x^16+264x^18+376x^20+120x^22+42x^24
The gray image is a linear code over GF(2) with n=76, k=10 and d=32.
This code was found by Heurico 1.16 in 0.0144 seconds.