The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2  X X^2 X^2
 0  0  X  0  X  X  X X^2  0 X^2  0  X X^2+X X^2+X  X  0
 0  0  0  X  X X^2 X^2+X X^2+X  0 X^2+X  X  0 X^2+X X^2  0 X^2+X
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  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+74x^12+16x^13+198x^14+112x^15+241x^16+112x^17+172x^18+16x^19+66x^20+14x^22+2x^24

The gray image is a linear code over GF(2) with n=64, k=10 and d=24.
This code was found by Heurico 1.16 in 0.0125 seconds.