The generator matrix

 1  0  0  0  1  1  1 X^2+X X^2  1  X  X  1  1 X^2  1  1  1  1  1  1
 0  1  0  0  0  1  1  1  X X^2+X  1  1 X^2 X^2+1 X^2+X  0  1  1 X^2 X+1  0
 0  0  1  0  1  1  0 X+1  1 X^2+X  1 X^2 X^2+X+1 X^2+X  0  1 X^2+X+1 X^2 X^2+1  0  0
 0  0  0  1  1  0 X+1  1  1 X+1  X X+1  X  X  1  0 X^2  0 X+1 X^2+X+1  0
 0  0  0  0  X  0 X^2+X  X X^2+X X^2  X X^2  0 X^2+X X^2+X  X X^2+X X^2 X^2  X  0
 0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 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+62x^14+232x^15+785x^16+1352x^17+2347x^18+3800x^19+4981x^20+5536x^21+4987x^22+3992x^23+2463x^24+1224x^25+657x^26+232x^27+87x^28+16x^29+11x^30+3x^32

The gray image is a linear code over GF(2) with n=84, k=15 and d=28.
This code was found by Heurico 1.16 in 7.01 seconds.