The generator matrix

 1  0  1  1  1 X^2  1  1 X^2  1  1 X^2 X^2+X  0  1  1
 0  1  1  0  1  1 X+1 X^2  1 X^2+X X^2+1  1  1  X  0  1
 0  0  X  0  0  0  0  X  X X^2+X X^2+X  X X^2  X X^2  0
 0  0  0  X  0  X  X  X X^2+X X^2 X^2+X X^2+X  X  X X^2  X
 0  0  0  0  X X^2  X X^2+X X^2+X  X X^2  X X^2+X  0  X 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+64x^11+129x^12+234x^13+496x^14+716x^15+807x^16+732x^17+485x^18+256x^19+117x^20+42x^21+10x^22+4x^23+2x^24+1x^26

The gray image is a linear code over GF(2) with n=64, k=12 and d=22.
This code was found by Heurico 1.16 in 0.105 seconds.