The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+172x^14+288x^15+708x^16+840x^17+1412x^18+1312x^19+1471x^20+880x^21+668x^22+256x^23+151x^24+8x^25+20x^26+5x^28

The gray image is a linear code over GF(2) with n=76, k=13 and d=28.
This code was found by Heurico 1.16 in 0.594 seconds.