The generator matrix

 1  0  0  1  1  1  X  X X^2  0  1  1  1  1  1  X  1 X^2  1
 0  1  0  1 X^2 X^2+1  1  1  1  X  1 X^2  X X^2+X X+1 X^2 X^2+X+1  1  0
 0  0  1 X^2  1 X^2+1 X^2+1 X^2+X+1  X  1 X^2+X X^2+X+1 X+1 X^2 X^2+X+1  X  X X+1  1

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+41x^16+94x^17+106x^18+88x^19+54x^20+56x^21+38x^22+16x^23+16x^24+2x^25

The gray image is a linear code over GF(2) with n=76, k=9 and d=32.
This code was found by Heurico 1.11 in 3.81e-009 seconds.