The generator matrix

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

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+172x^11+541x^12+1032x^13+1857x^14+2882x^15+3351x^16+2920x^17+1978x^18+1016x^19+425x^20+160x^21+37x^22+10x^23+2x^24

The gray image is a linear code over GF(2) with n=64, k=14 and d=22.
This code was found by Heurico 1.13 in 0.515 seconds.