The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  1  1 X^2+X  0 X^2+X  0 X^2+X  1  1
 0  1  0  0  0  1  1  1  X X+1 X^2+1 X^2+X X^2  1  1  1  1  1 X^2+1
 0  0  1  0  1  1  X X+1  0  X X+1  1 X^2 X+1  1 X^2  X  X X^2+1
 0  0  0  1  1  0 X+1  1  1 X^2  1 X^2+X  1 X^2+1  X  1 X^2+X X+1 X^2
 0  0  0  0  X  0  0  0 X^2 X^2+X X^2+X  X  X X^2+X  0 X^2 X^2+X  X  X
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  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+154x^13+467x^14+1212x^15+2339x^16+3676x^17+5334x^18+6208x^19+5508x^20+3884x^21+2269x^22+1084x^23+440x^24+156x^25+25x^26+8x^27+2x^29+1x^34

The gray image is a linear code over GF(2) with n=76, k=15 and d=26.
This code was found by Heurico 1.16 in 6.45 seconds.