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.