The generator matrix
1 0 0 0 1 1 1 X^2 1 X^2 1 X 1 1 X X^2
0 1 0 0 0 1 1 1 X^2+X+1 1 X^2 X^2+X X^2+1 X^2+X X^2 0
0 0 1 0 1 1 X X+1 X X+1 0 1 0 X+1 X^2 X
0 0 0 1 1 0 X+1 1 X^2+X 0 X+1 1 X+1 X^2+1 1 1
0 0 0 0 X X^2 0 X^2 X X X^2+X 0 X 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+172x^11+541x^12+1032x^13+1857x^14+2882x^15+3351x^16+2920x^17+1978x^18+1016x^19+425x^20+160x^21+37x^22+10x^23+2x^24
The gray image is a linear code over GF(2) with n=64, k=14 and d=22.
This code was found by Heurico 1.13 in 0.515 seconds.