The generator matrix

 1  0  0  0  0  1  1  1 X^2  1  X X^2+X  1 X^2+X  1  0  0  1  1
 0  1  0  0  0 X^2  1 X^2+1  1  1  1 X^2  X X^2+X X^2+X X^2+X  1  X  0
 0  0  1  0  0 X^2+X+1 X+1  X X^2+X+1  1  X  1  0  1 X^2+X  1 X^2+X X+1  X
 0  0  0  1  0  1  X X^2+1 X^2+X+1 X^2+X+1 X+1  1 X+1 X^2+X+1 X^2+X+1 X^2  1 X^2+X  X
 0  0  0  0  1  1 X^2  X  X X+1 X^2+1 X^2+1 X+1 X^2+X  0 X^2+X+1  0 X^2+1 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+84x^13+616x^14+1136x^15+2355x^16+3676x^17+5363x^18+5962x^19+5705x^20+3972x^21+2286x^22+908x^23+514x^24+124x^25+55x^26+10x^27+1x^28

The gray image is a linear code over GF(2) with n=76, k=15 and d=26.
This code was found by Heurico 1.13 in 2.31 seconds.