The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1
 0  X  0  0  0  0  0 X^2 X^2  X X^2+X X^2+X X^2+X  0 X^2 X^2+X
 0  0  X  0  0 X^2 X^2+X  X  X  X  X X^2+X  X X^2+X X^2+X X^2
 0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X X^2+X  0 X^2  X  X
 0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2  0 X^2+X X^2  0  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+36x^11+97x^12+104x^13+128x^14+380x^15+573x^16+368x^17+128x^18+92x^19+94x^20+40x^21+4x^23+2x^24+1x^28

The gray image is a linear code over GF(2) with n=64, k=11 and d=22.
This code was found by Heurico 1.16 in 0.0385 seconds.