The generator matrix
1 0 0 0 1 1 1 1 X 1 0 1 X^2 1 X 1 1
0 1 0 0 0 X+1 X^2+1 X 1 X^2+X+1 X^2+X X^2+1 1 X^2+X+1 1 X+1 X
0 0 1 0 1 X^2+1 1 1 X 0 1 X^2 X^2+1 X+1 1 X^2 X+1
0 0 0 1 1 X^2+X+1 0 X^2 1 X^2 X^2+X+1 1 0 X 1 1 X
0 0 0 0 X X X^2+X X^2 X X^2+X X^2+X 0 X^2 0 X^2 X^2 0
generates a code of length 17 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+257x^12+420x^13+1430x^14+1440x^15+3312x^16+2360x^17+3668x^18+1584x^19+1335x^20+324x^21+214x^22+16x^23+23x^24
The gray image is a linear code over GF(2) with n=68, k=14 and d=24.
This code was found by Heurico 1.13 in 0.562 seconds.