The generator matrix

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

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+17x^16+28x^17+85x^18+16x^19+76x^20+16x^21+4x^22+2x^24+4x^25+6x^26+1x^34

The gray image is a linear code over GF(2) with n=76, k=8 and d=32.
This code was found by Heurico 1.16 in 0.00339 seconds.