The generator matrix

 1  0  0  1  1  1  X  1  1  0 X^2  1  1  1 X^2 X^2+X X^2  1  1  1 X^2
 0  1  0  1 X^2+X X^2+X+1  1  1 X^2  1  0 X^2 X^2+1  X  1  1  1  0 X^2+X X^2+1  1
 0  0  1  1  1  0 X+1  1  0 X^2  1 X+1 X^2+X  1  1 X^2+X+1 X^2+X  0 X+1 X^2 X^2+X+1
 0  0  0  X X^2+X X^2+X X^2+X X^2 X^2+X  X  X  X  X  0  0 X^2  X X^2  X  0  X
 0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 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+200x^16+304x^17+660x^18+920x^19+1419x^20+1168x^21+1504x^22+864x^23+631x^24+320x^25+172x^26+8x^27+17x^28+4x^32

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 2.76 seconds.