The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+74x^15+201x^16+252x^17+312x^18+382x^19+344x^20+248x^21+128x^22+54x^23+30x^24+12x^25+8x^26+2x^27

The gray image is a linear code over GF(2) with n=76, k=11 and d=30.
This code was found by Heurico 1.16 in 28.7 seconds.