The generator matrix

 1  0  0  1  1  1 X^2  1  1  1 X^2+X X^2+X  1  1  1  X
 0  1  0  1  X X^2+X+1  1  0 X^2 X+1  1  1 X^2+X X^2+X+1 X^2  0
 0  0  1  1  1  0 X+1  X X+1 X^2+X+1 X^2 X+1  1  1  0  0
 0  0  0  X  0 X^2+X  X X^2+X X^2+X X^2  0 X^2 X^2+X  0  0  X
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0  0  0  0 X^2 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 11.

Homogenous weight enumerator: w(x)=1x^0+84x^11+327x^12+488x^13+1060x^14+1212x^15+1811x^16+1232x^17+1128x^18+492x^19+256x^20+72x^21+20x^22+4x^23+4x^24+1x^28

The gray image is a linear code over GF(2) with n=64, k=13 and d=22.
This code was found by Heurico 1.16 in 3.93 seconds.