The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1  X X^2  0 X^2+X  1  1
 0  1  0  1  0 X^2+X+1  1  1 X^2  X  0  1  1  1  1  X
 0  0  1  1  1  0  1  1  0 X^2+1  1 X+1  X X^2+1 X^2 X^2+1
 0  0  0  X  0  0  0 X^2  X  X X^2+X X^2 X^2+X X^2+X X^2  X
 0  0  0  0  X X^2+X X^2+X  0 X^2  X X^2 X^2+X X^2  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+70x^11+255x^12+552x^13+968x^14+1430x^15+1635x^16+1424x^17+1008x^18+546x^19+216x^20+72x^21+8x^22+2x^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 0.434 seconds.