The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X
0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2
0 0 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0
0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2
0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2
0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0
0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2
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+78x^16+96x^18+256x^19+32x^22+48x^24+1x^32
The gray image is a linear code over GF(2) with n=76, k=9 and d=32.
This code was found by Heurico 1.16 in 0.00699 seconds.