The generator matrix
1 1 1 1 1 1 1 1 1 X 1 X 1 1
0 X 0 0 0 0 0 0 X^2 X^2+X X^2+X X^2+X X^2 X^2
0 0 X 0 0 0 X X^2+X X^2+X X X^2+X X X 0
0 0 0 X 0 X X X^2+X 0 0 X^2 X^2+X 0 X
0 0 0 0 X X 0 X^2+X X X X X^2 0 0
0 0 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2
0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0
0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2
generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+262x^8+740x^10+2336x^12+2048x^13+5572x^14+2048x^15+2413x^16+716x^18+232x^20+12x^22+4x^24
The gray image is a linear code over GF(2) with n=56, k=14 and d=16.
This code was found by Heurico 1.16 in 1.3 seconds.