The generator matrix

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

generates a code of length 21 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+116x^16+416x^17+733x^18+912x^19+1175x^20+1392x^21+1305x^22+1040x^23+607x^24+304x^25+135x^26+32x^27+21x^28+3x^30

The gray image is a linear code over GF(2) with n=84, k=13 and d=32.
This code was found by Heurico 1.16 in 0.544 seconds.