The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1 X^2  X  X  X  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X X^2 X^2  X  0 X^2 X^2+X  X  0
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0 X^2  0  0  X X^2  X X^2  0
 0  0  0  X  0  X  X  X  0 X^2+X X^2 X^2 X^2+X  X  X X^2+X X^2  0 X^2+X X^2  0
 0  0  0  0  X  X  0  X X^2+X  X  0 X^2 X^2 X^2+X X^2  X X^2+X X^2+X  0  X  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 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+63x^14+136x^15+236x^16+344x^17+581x^18+884x^19+1156x^20+1336x^21+1190x^22+932x^23+592x^24+360x^25+202x^26+92x^27+60x^28+8x^29+11x^30+4x^31+3x^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 0.879 seconds.