The generator matrix

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

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+30x^14+44x^15+131x^16+188x^17+295x^18+460x^19+558x^20+652x^21+582x^22+484x^23+312x^24+180x^25+104x^26+36x^27+18x^28+4x^29+12x^30+4x^32+1x^34

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 0.188 seconds.