The generator matrix

 1  0  0  0  1  1  1 X^2 X^2+X  1  1  1  0  1  X  1
 0  1  0  0  0  1 X^2+1  1  1  X X^2+X+1 X^2+X+1  0 X+1 X^2 X^2
 0  0  1  0  1  1  X  1  0  X  1  0  1 X^2  0  0
 0  0  0  1  1 X^2+X X+1  1  1 X+1 X+1 X^2+X X+1  X X^2 X^2
 0  0  0  0  X  0  X X^2+X X^2+X X^2 X^2 X^2 X^2 X^2+X  X X^2+X
 0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 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+104x^10+348x^11+999x^12+2144x^13+4007x^14+5696x^15+6116x^16+5716x^17+4107x^18+2140x^19+941x^20+328x^21+101x^22+8x^23+7x^24+4x^25+1x^26

The gray image is a linear code over GF(2) with n=64, k=15 and d=20.
This code was found by Heurico 1.16 in 4.25 seconds.