The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1  1  1 X^2  1  1  0 X^2  1  1
 0  1  0  X  1 X+1  1 X^2 X^2+X+1 X+1 X^2+X X^2  X  X X^2+1  1 X^2+X  X  X
 0  0  1  1 X^2+X+1  0 X^2+X+1  X  X X+1 X+1  1  1  X  0 X+1  1  1  X
 0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 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+14x^13+147x^14+314x^15+477x^16+1082x^17+1174x^18+1774x^19+1172x^20+1122x^21+460x^22+278x^23+138x^24+22x^25+10x^26+2x^27+4x^28+1x^30

The gray image is a linear code over GF(2) with n=76, k=13 and d=26.
This code was found by Heurico 1.16 in 17.9 seconds.