The generator matrix

 1  1  1  1  X  1  1  0  1  1  X  X  1  1  1  1  1  1  1
 0  X  0 X^2+X  X  0 X^2+X  X  0 X^2+X  X X^2+X  0  0  0  0  0  0  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0
 0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0  0 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0  0  0
 0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0  0
 0  0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0
 0  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0
 0  0  0  0  0  0  0  0  0  0 X^2 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 8.

Homogenous weight enumerator: w(x)=1x^0+113x^8+56x^10+448x^12+315x^14+256x^15+1235x^16+1024x^17+3976x^18+1536x^19+3976x^20+1024x^21+1235x^22+256x^23+315x^24+448x^26+56x^28+113x^30+1x^38

The gray image is a linear code over GF(2) with n=76, k=14 and d=16.
This code was found by Heurico 1.16 in 0.648 seconds.