The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X
0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2
0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2
0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0
0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 0
0 0 0 0 0 X^2 0 0 0 0 X^2 0 0 X^2
0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2
0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0
0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2
0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2
generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+28x^6+77x^8+112x^10+424x^12+2792x^14+459x^16+112x^18+56x^20+28x^22+7x^24
The gray image is a linear code over GF(2) with n=56, k=12 and d=12.
This code was found by Heurico 1.16 in 0.0327 seconds.