The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1 X^2  1  X X^2  1  1  1  0  1
 0  1  1 X^2+X X^2+X+1  1 X^2 X+1  X X^2+1  1  0  1  1 X^2+X+1 X^2+X X^2  0  0
 0  0  X  0 X^2+X  0  X  0  X X^2  X X^2  X X^2+X X^2+X X^2  X  X  0
 0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2
 0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  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+24x^14+78x^15+124x^16+344x^17+240x^18+470x^19+235x^20+288x^21+112x^22+90x^23+23x^24+8x^25+8x^26+2x^27+1x^28

The gray image is a linear code over GF(2) with n=76, k=11 and d=28.
This code was found by Heurico 1.16 in 0.0377 seconds.