The generator matrix

 1  1  1  1  1  1  1  1  X  1  X  1  X  X  X  X  X X^2  1
 0  X  0  0  0  0  0  0 X^2+X  X  X X^2  X  0  X X^2 X^2  0  0
 0  0  X  0  0  0  0 X^2  0 X^2 X^2 X^2+X X^2+X  X  0  0  X  X  0
 0  0  0  X  0  0 X^2  X  X X^2  X  0 X^2+X  X X^2 X^2  0  0  0
 0  0  0  0  X  0 X^2+X X^2+X X^2 X^2+X  X  X  X  X  0  X  X  0  0
 0  0  0  0  0  X  X X^2 X^2+X  0 X^2+X X^2  0  X X^2+X X^2+X X^2 X^2+X  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+87x^12+94x^13+244x^14+356x^15+581x^16+916x^17+1103x^18+1348x^19+1176x^20+960x^21+601x^22+332x^23+222x^24+76x^25+65x^26+12x^27+13x^28+2x^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 0.748 seconds.