The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  X  X
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X^2+X X^2+X  0
 0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0
 0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 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+72x^12+32x^13+148x^14+96x^15+317x^16+96x^17+168x^18+32x^19+56x^20+4x^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 0.00856 seconds.