The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  0  X  1  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1  0  0  0  0
 0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0
 0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2  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  0 X^2  0 X^2 X^2  0 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+35x^12+8x^13+105x^14+48x^15+351x^16+376x^17+791x^18+672x^19+788x^20+376x^21+348x^22+48x^23+104x^24+8x^25+32x^26+1x^28+3x^30+1x^34

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 0.0959 seconds.