The generator matrix

 1  1  1  1  1  1  1  1  X  0  1  X  1  0  1  1  X  X  1  X  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X  X  X X^2 X^2+X X^2+X  X  0 X^2+X  0 X^2+X  0  0  X
 0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0
 0  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2
 0  0  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  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+77x^14+193x^16+403x^18+256x^19+817x^20+512x^21+902x^22+256x^23+474x^24+138x^26+46x^28+13x^30+4x^32+3x^34+1x^36

The gray image is a linear code over GF(2) with n=84, k=12 and d=28.
This code was found by Heurico 1.16 in 0.322 seconds.