The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  1  1 X^2  1  X  1  X  1
 0  X  0  X  0  0  X X^2+X X^2  X X^2+X X^2  X  X  0  X X^2+X  0  0
 0  0  X  X  0 X^2+X  X  0  X  X  0  X X^2+X  X  0 X^2+X  0 X^2  0
 0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0
 0  0  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  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+53x^12+38x^13+107x^14+122x^15+336x^16+206x^17+1038x^18+274x^19+1036x^20+242x^21+356x^22+110x^23+94x^24+26x^25+34x^26+6x^27+15x^28+1x^30+1x^32

The gray image is a linear code over GF(2) with n=76, k=12 and d=24.
This code was found by Heurico 1.16 in 0.137 seconds.