The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1 X^2  1
 0  X  0  X  0 X^2  X X^2+X  0  X X^2 X^2  0  X X^2+X X^2+X  X  X  0
 0  0  X  X  0  X X^2+X X^2 X^2  X X^2+X X^2  X X^2+X X^2+X  0  0 X^2+X  0
 0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  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+19x^16+68x^17+15x^18+64x^19+12x^20+56x^21+12x^22+4x^25+4x^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 0.00473 seconds.