The generator matrix

 1  0  0  1  1  1  X  1  1 X^2  X  1  X X^2  1  1
 0  1  0  1 X^2+X X^2+X+1  1 X^2+1 X^2+1  1  1  0  1  1 X^2  X
 0  0  1  1 X^2+X+1  X  1 X+1  0  X X^2+X+1 X+1 X^2+X X^2+X  1 X^2+1
 0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2
 0  0  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2

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+38x^12+218x^13+184x^14+428x^15+327x^16+432x^17+180x^18+180x^19+30x^20+22x^21+4x^22+4x^24

The gray image is a linear code over GF(2) with n=64, k=11 and d=24.
This code was found by Heurico 1.16 in 0.0249 seconds.