The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X 0 X X 1 1
0 X 0 0 0 0 0 0 0 X X^2+X X X^2 X X X^2+X X^2 X^2 X
0 0 X 0 0 0 X X^2+X X X X 0 X X^2 X 0 X X^2 0
0 0 0 X 0 X X X X^2 0 0 X^2 X 0 X X^2+X X X^2 X
0 0 0 0 X X X^2 X^2+X X^2+X 0 X X X X^2+X X^2 X^2+X X^2+X X^2 0
0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0
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+52x^13+113x^14+152x^15+243x^16+454x^17+683x^18+724x^19+648x^20+474x^21+247x^22+144x^23+96x^24+42x^25+13x^26+4x^27+4x^28+2x^29
The gray image is a linear code over GF(2) with n=76, k=12 and d=26.
This code was found by Heurico 1.16 in 0.203 seconds.