The generator matrix
1 1 1 1 1 1 1 1 1 1 X 1 1 X X 1
0 X^2 0 0 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 0 X^2 X^2 X^2 0 0
0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0
0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0
0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0
0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0
0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 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 0 0 X^2 X^2 X^2 0 0 X^2 0
generates a code of length 16 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+77x^8+28x^10+168x^12+128x^13+112x^14+384x^15+2251x^16+384x^17+232x^18+128x^19+56x^20+112x^22+7x^24+28x^26
The gray image is a linear code over GF(2) with n=64, k=12 and d=16.
This code was found by Heurico 1.16 in 0.0498 seconds.