The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+22x^13+47x^14+70x^15+193x^16+102x^17+526x^18+118x^19+540x^20+114x^21+184x^22+66x^23+30x^24+18x^25+10x^26+2x^27+4x^28+1x^30

The gray image is a linear code over GF(2) with n=76, k=11 and d=26.
This code was found by Heurico 1.16 in 0.143 seconds.