The generator matrix
1 0 0 0 0 1 1 1 X^2 1 X X^2 X 1 1 1 X^2+X 0 1
0 1 0 0 0 0 X^2+1 X+1 1 X^2+1 1 X 1 X^2+1 X^2 X 1 1 0
0 0 1 0 0 1 1 X 1 X^2+1 0 1 X^2+X+1 1 X+1 X^2+X X X^2+X+1 X^2
0 0 0 1 0 1 X^2 0 X^2+X X^2+1 X+1 X^2+X+1 X^2+X+1 X^2+1 X X^2+X+1 X^2 X 0
0 0 0 0 1 1 X^2+X 1 X+1 X^2+X+1 X^2+X 0 X^2+X+1 X X^2+X+1 1 1 X^2+1 X^2
0 0 0 0 0 X 0 X^2 0 X^2 X^2 X^2 X X^2+X X 0 X^2+X X^2+X 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+134x^12+714x^13+1670x^14+4658x^15+8426x^16+16392x^17+20771x^18+25930x^19+19961x^20+16644x^21+8683x^22+4710x^23+1617x^24+552x^25+169x^26+30x^27+5x^28+2x^29+3x^30
The gray image is a linear code over GF(2) with n=76, k=17 and d=24.
This code was found by Heurico 1.13 in 28 seconds.