The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  X
 0  X  0 X^2+X  0 X^2+X X^2 X^2+X  0  0  0 X^2+X X^2+X X^2+X X^2+X X^2
 0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2
 0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2
 0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  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+44x^12+16x^13+42x^14+48x^15+207x^16+48x^17+52x^18+16x^19+32x^20+2x^22+4x^24

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 0.00428 seconds.