The generator matrix

 1  0  0  0  0  1  1  1  X  1  1  1  1  1  1  1
 0  1  0  0  0  0 X^2 X^2  0 X^2+1 X+1 X^2+X X^2+1 X^2+X+1 X+1  X
 0  0  1  0  0  0 X^2+1 X+1  1 X^2  X X^2+1 X+1 X^2+X+1 X^2+1  X
 0  0  0  1  0  1 X+1  X  1 X^2+1  X  0 X^2+X X^2  1  0
 0  0  0  0  1  1  X X+1 X+1  X  0  X X^2+X  1 X^2+1  0
 0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  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+170x^10+586x^11+1927x^12+4260x^13+7255x^14+12058x^15+12898x^16+12072x^17+7565x^18+4206x^19+1737x^20+596x^21+177x^22+14x^23+13x^24+1x^26

The gray image is a linear code over GF(2) with n=64, k=16 and d=20.
This code was found by Heurico 1.13 in 4.94 seconds.