The generator matrix

 1  0  0  0  1  1  1  0 X^2  1  1  1  X  X  1  1  0  1  1
 0  1  0  0  0  1  1  1  1  X X^2+X X^2+1  0 X^2 X^2+X+1  1  1 X+1  1
 0  0  1  0  1  0 X^2+1  1  1  1 X^2  X  1  1 X^2+X+1 X^2+X X^2+X  1  1
 0  0  0  1  1 X^2+1 X^2 X+1  X X^2+X X+1  0 X^2+1  0  1 X^2+X X^2+1 X^2+X  1
 0  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2  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+82x^14+396x^15+601x^16+948x^17+1380x^18+1384x^19+1362x^20+1016x^21+570x^22+332x^23+82x^24+20x^25+16x^26+2x^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 1.11 in 0.188 seconds.