The generator matrix

 1  0  0  1  1  1 X^2+X  1  1 X^2  1  X X^2  1  1  1  1  1  1
 0  1  0  1  0  1  1 X^2+X X+1  1 X^2 X^2  1 X^2 X^2+1 X^2+1  1  0  0
 0  0  1  1  1  0  1 X+1 X+1  X  0  1 X+1 X^2+1  0 X^2+X X^2+1  X  0
 0  0  0  X  0  0  0  0  0  X X^2+X  X X^2 X^2 X^2+X X^2+X X^2  0  0
 0  0  0  0  X  0  0  X X^2  0  X X^2 X^2+X X^2 X^2+X  X X^2+X X^2+X X^2+X
 0  0  0  0  0  X X^2+X  X X^2 X^2+X X^2+X  0 X^2  X  0  X X^2+X X^2 X^2+X

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+50x^12+186x^13+418x^14+1060x^15+2227x^16+3840x^17+5507x^18+6180x^19+5480x^20+3892x^21+2245x^22+1068x^23+392x^24+144x^25+53x^26+12x^27+10x^28+2x^29+1x^30

The gray image is a linear code over GF(2) with n=76, k=15 and d=24.
This code was found by Heurico 1.16 in 5.97 seconds.