The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+34x^12+74x^13+151x^14+246x^15+548x^16+982x^17+1311x^18+1482x^19+1308x^20+998x^21+573x^22+250x^23+143x^24+58x^25+13x^26+6x^27+13x^28+1x^36

The gray image is a linear code over GF(2) with n=76, k=13 and d=24.
This code was found by Heurico 1.16 in 0.523 seconds.