The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1
0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2
0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0
0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0
0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2
0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0
0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0
generates a code of length 16 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+45x^12+32x^14+361x^16+32x^18+34x^20+6x^24+1x^28
The gray image is a linear code over GF(2) with n=64, k=9 and d=24.
This code was found by Heurico 1.16 in 0.00427 seconds.