The generator matrix

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

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+34x^11+104x^12+182x^13+223x^14+296x^15+363x^16+300x^17+245x^18+178x^19+76x^20+30x^21+9x^22+4x^23+3x^26

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 0.0358 seconds.