The generator matrix

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

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+103x^16+276x^18+128x^19+411x^20+256x^21+378x^22+128x^23+255x^24+80x^26+29x^28+2x^30+1x^32

The gray image is a linear code over GF(2) with n=84, k=11 and d=32.
This code was found by Heurico 1.16 in 0.0643 seconds.