The generator matrix

 1  1  1  1  1  1  1  X  1  1  X  1  1  0  1  1
 0  X  0  0  0  0  0  0  X X^2  X  0  X X^2  X  X
 0  0  X  0  0  0  0 X^2+X  X  0 X^2+X X^2+X X^2  X X^2+X  X
 0  0  0  X  0  0  0  X X^2+X X^2+X X^2 X^2+X X^2+X  0 X^2+X  0
 0  0  0  0  X  0  X X^2  X X^2+X X^2  0 X^2  0  0 X^2+X
 0  0  0  0  0  X  X X^2+X X^2  X X^2 X^2+X X^2+X  0 X^2  X
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0

generates a code of length 16 over Z2[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+54x^9+191x^10+234x^11+445x^12+770x^13+1579x^14+3034x^15+3718x^16+3038x^17+1665x^18+782x^19+423x^20+230x^21+145x^22+46x^23+21x^24+4x^25+4x^26

The gray image is a linear code over GF(2) with n=64, k=14 and d=18.
This code was found by Heurico 1.16 in 1.43 seconds.