The generator matrix

 1  0  0  0  0  1  1  1  1  X X^2+X X^2  1  1  1 X^2  1  1  1
 0  1  0  0  0  0  1  1 X^2+1  1 X^2  1  X X^2+X  X  1 X^2  0  0
 0  0  1  0  0 X+1 X+1  X  0  1 X^2 X^2+X+1 X^2+1  0 X^2+X X^2+X  X X^2  0
 0  0  0  1  0  1  X X+1  0  1  1 X^2+X  X  1  X X^2+X+1  1 X^2+X+1  0
 0  0  0  0  1  1 X^2  0 X+1  1 X^2+X+1  X X+1 X^2+1 X+1 X^2+X+1  0  1  0
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 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+103x^12+394x^13+1155x^14+2648x^15+4429x^16+7876x^17+10214x^18+11754x^19+10135x^20+8274x^21+4494x^22+2476x^23+1065x^24+352x^25+134x^26+18x^27+10x^28+3x^30+1x^32

The gray image is a linear code over GF(2) with n=76, k=16 and d=24.
This code was found by Heurico 1.13 in 7.25 seconds.