The generator matrix

 1  1  1  1  1  1  1  1  X  1  X  X  1  1  1  X  1  1  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  X  X X^2  X X^2+X X^2 X^2 X^2  0
 0  0  X  0  X  X X^2+X  0  0 X^2  X  0 X^2+X X^2  X X^2+X  X  0  0
 0  0  0  X  X  0 X^2+X  X  X  0 X^2 X^2+X  0 X^2+X  0  X X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  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+40x^12+42x^13+122x^14+104x^15+194x^16+422x^17+714x^18+916x^19+552x^20+406x^21+290x^22+128x^23+100x^24+26x^25+22x^26+4x^27+8x^28+4x^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 0.145 seconds.