The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  X  X  1  1  0  1  1  1  1  1
 0  X  0  0  0  X X^2+X  X  0  0 X^2 X^2  X  X  X  X  0  0  0 X^2  0
 0  0  X  0  X  X X^2+X  0  0 X^2  X X^2+X  X  0 X^2  X X^2 X^2  X  X  0
 0  0  0  X  X  0 X^2+X  X X^2  X  0  X  0 X^2+X  0 X^2+X X^2  X X^2+X  0  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0
 0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 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+45x^14+46x^15+121x^16+128x^17+224x^18+470x^19+571x^20+760x^21+773x^22+474x^23+153x^24+128x^25+99x^26+34x^27+49x^28+8x^29+10x^30+1x^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 0.192 seconds.