The generator matrix

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

generates a code of length 21 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+100x^14+409x^16+96x^17+931x^18+384x^19+1630x^20+1088x^21+1598x^22+384x^23+1044x^24+96x^25+300x^26+114x^28+14x^30+2x^32+1x^34

The gray image is a linear code over GF(2) with n=84, k=13 and d=28.
This code was found by Heurico 1.16 in 0.885 seconds.