The generator matrix

 1  0  1  1  1 X^2+X  1 X^2  1  1 X^2  1  X X^2 X^2  1
 0  1  1 X^2+X X^2+X+1  1 X^2  1 X+1  X  1 X+1 X^2  X  X  0
 0  0  X  0 X^2+X X^2  X  X  0 X^2+X X^2+X X^2  X X^2+X X^2  0
 0  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 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+42x^12+122x^13+60x^14+282x^15+55x^16+244x^17+56x^18+100x^19+30x^20+18x^21+12x^22+2x^23

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 0.00898 seconds.