The generator matrix
1 1 1 1 1 1 1 1 X X 1 1 X 1
0 X 0 0 0 0 0 X^2 X^2+X X^2+X X^2+X X^2+X X^2 X
0 0 X 0 0 X^2 X^2+X X X^2+X 0 X X X^2 X
0 0 0 X 0 X^2+X X^2+X X 0 X^2 X^2 X X 0
0 0 0 0 X X X^2 X^2+X X^2+X 0 X^2+X X X 0
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+28x^9+79x^10+114x^11+190x^12+374x^13+475x^14+372x^15+215x^16+104x^17+53x^18+26x^19+10x^20+6x^21+1x^22
The gray image is a linear code over GF(2) with n=56, k=11 and d=18.
This code was found by Heurico 1.16 in 0.0402 seconds.