The generator matrix
1 1 1 1 1 1 1 1 X 1 X^2 X X 1 X 1
0 X 0 0 0 0 0 0 X^2+X X X X^2 X^2 X^2 X^2 X
0 0 X 0 0 0 X X^2+X X X X^2 X X^2 0 X^2 X
0 0 0 X 0 X X X X^2 X^2 X^2 X^2 X 0 X^2+X 0
0 0 0 0 X X X^2 X^2+X X^2+X X^2 X^2+X 0 X^2+X 0 X^2 0
0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 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+43x^10+74x^11+141x^12+280x^13+469x^14+598x^15+730x^16+820x^17+487x^18+214x^19+143x^20+48x^21+23x^22+10x^23+9x^24+4x^25+2x^26
The gray image is a linear code over GF(2) with n=64, k=12 and d=20.
This code was found by Heurico 1.16 in 0.113 seconds.