The generator matrix

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

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+48x^12+106x^13+203x^14+382x^15+601x^16+886x^17+1148x^18+1294x^19+1312x^20+986x^21+522x^22+362x^23+206x^24+66x^25+44x^26+10x^27+8x^28+4x^29+3x^30

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 0.725 seconds.