The generator matrix

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

generates a code of length 16 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+130x^10+440x^11+1046x^12+2344x^13+3548x^14+5876x^15+5921x^16+5952x^17+3562x^18+2416x^19+1006x^20+376x^21+120x^22+4x^23+26x^24

The gray image is a linear code over GF(2) with n=64, k=15 and d=20.
This code was found by Heurico 1.13 in 1.52 seconds.