The generator matrix
1 0 0 0 1 1 1 X^2 0 1 1 1 X^2+X 1
0 1 0 0 0 X^2+1 X+1 1 1 X^2+1 X^2+1 X 1 X
0 0 1 0 1 1 X X+1 X X+1 X^2 1 X^2+X+1 X^2+1
0 0 0 1 1 X 1 1 X+1 X 0 X 0 1
0 0 0 0 X 0 0 X^2 X X^2+X X X^2 0 X
generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+82x^9+458x^10+988x^11+1837x^12+2992x^13+3537x^14+3120x^15+1997x^16+906x^17+324x^18+100x^19+37x^20+4x^21+1x^22
The gray image is a linear code over GF(2) with n=56, k=14 and d=18.
This code was found by Heurico 1.13 in 0.359 seconds.