The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+84x^15+156x^16+354x^17+220x^18+418x^19+261x^20+340x^21+112x^22+72x^23+11x^24+10x^25+4x^26+2x^27+3x^28

The gray image is a linear code over GF(2) with n=76, k=11 and d=30.
This code was found by Heurico 1.16 in 0.0346 seconds.